{"id":57940,"date":"2019-12-12T14:33:19","date_gmt":"2019-12-12T14:33:19","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=57940"},"modified":"2026-03-25T11:55:20","modified_gmt":"2026-03-25T16:55:20","slug":"lines-and-planes","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/lines-and-planes\/","title":{"rendered":"Lines and Planes"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_SifTub1Tp1Q\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_SifTub1Tp1Q\" data-source-videoID=\"SifTub1Tp1Q\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Lines and Planes Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Lines and Planes\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_SifTub1Tp1Q:hover {cursor:pointer;} img#videoThumbnailImage_SifTub1Tp1Q {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/360-lines-and-planes-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_SifTub1Tp1Q\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_SifTub1Tp1Q\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Lines and Planes\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_SifTub1Tp1Q\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_SifTub1Tp1Q\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_SifTub1Tp1Q\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction 7fM_Function() {\n  var x = document.getElementById(\"7fM\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"7fM_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"7fM\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Points,_Lines,_and_Planes\" class=\"smooth-scroll\">Points, Lines, and Planes<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Other_Important_Terms\" class=\"smooth-scroll\">Other Important Terms<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Lines_and_Planes_Practice_Questions\" class=\"smooth-scroll\">Lines and Planes Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on lines and planes!<\/p>\n<p>The study of geometry is very much language-based, meaning that there are countless terms, relationships, and figures with meanings that are dependent on an understanding of other concepts. It can get pretty confusing if the foundational terms are not understood.<\/p>\n<p>In this video, we\u2019re going to start with the most basic figures: a point, a line, and a plane. These \u201cundefined\u201d terms are described, rather than being defined, and they support the definitions of all other geometric terms.<\/p>\n<h2><span id=\"Points,_Lines,_and_Planes\" class=\"m-toc-anchor\"><\/span>Points, Lines, and Planes<\/h2>\n<h3><span id=\"Points\" class=\"m-toc-anchor\"><\/span>Points<\/h3>\n<p>\nTo start off, what is a point?<\/p>\n<p>A point is described as a very specific location, or position, in a plane. The notation for a point is a dot, but that dot does not have any dimension (length, width, circumference). A point is named with a capital letter, as in \u201cpoint A\u201d<\/p>\n<h3><span id=\"Lines\" class=\"m-toc-anchor\"><\/span>Lines<\/h3>\n<p>\nA line is described as a \u201cpath,\u201d as if a point was dragged or is moving. A straight line extends infinitely in opposite directions. <\/p>\n<p>A line is typically named with a lowercase letter, or by referencing two points on the line, with a line symbol above. The line notation has arrows on either end to indicate that they extend forever. Points that lie on a line are referred to as collinear. <br \/>\n<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/image_334.png\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<h3><span id=\"Planes\" class=\"m-toc-anchor\"><\/span>Planes<\/h3>\n<p>\nA plane surface has length and width, and extends infinitely in all directions. A flat surface, like a wall, floor, or ceiling, can be imagined as finite planes where geometric figures, like points and lines, can be drawn. <\/p>\n<p>A plane is typically named with a letter in script or italics (plane m) or by naming three points that lie on the plane, (plane ABC). Using three points in the naming of a plane lends to the perception of a two-dimensional surface. Points that lie in the same plane are said to be coplanar.<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/image_335.png\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<p>Planes that intersect do so at a line, and it is possible for three planes to intersect at exactly one point.<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/image_331.png\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<h2><span id=\"Other_Important_Terms\" class=\"m-toc-anchor\"><\/span>Other Important Terms<\/h2>\n<p>\nNow that we know these basic components, we can build our knowledge with terms that incorporate them in their definitions.<\/p>\n<h3><span id=\"Line_Segments\" class=\"m-toc-anchor\"><\/span>Line Segments<\/h3>\n<p>\nA line segment is the portion of a line that lies between two points on the line. The two points are called endpoints, and are included in the line segment, as are all the points that are between them. A line segment with endpoints A and B would be referenced as \\(\\overline{AB}\\).<\/p>\n<h3><span id=\"Rays\" class=\"m-toc-anchor\"><\/span>Rays<\/h3>\n<p>\nA ray starts at one point and extends infinitely in one direction on a plane. The ray symbol has one arrow indicating the starting point and the direction of the ray.<\/p>\n<h3><span id=\"Intersecting_Lines\" class=\"m-toc-anchor\"><\/span>Intersecting Lines<\/h3>\n<p>\nWhen two lines on a plane cross each other, they are referred to as intersecting lines. Intersecting lines on a plane cross at exactly one point.<\/p>\n<p>Because a line segment has length that can be measured between the endpoints, the exact midpoint of the segment can be determined. A point, line, or ray, or plane that crosses a line segment at the midpoint is called a bisector.<\/p>\n<h3><span id=\"Perpendicular_Lines\" class=\"m-toc-anchor\"><\/span>Perpendicular Lines<\/h3>\n<p>\nIntersecting lines on a plane that cross at 90\u00b0 angles, or \u201cright angles,\u201d are <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/parallel-and-perpendicular-lines\/\">perpendicular<\/a> to each other. <br \/>\n<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/image_333.png\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><br \/>\nExamples of perpendicular lines can be found on window panes, or on door frames.<\/p>\n<h3><span id=\"Parallel_Lines\" class=\"m-toc-anchor\"><\/span>Parallel Lines<\/h3>\n<p>\nLines on a plane that never cross are called parallel. These lines are exactly the same distance apart at all points, like the double yellow lines on a road, or tire tracks of a car.<\/p>\n<h3><span id=\"Transversal_Lines\" class=\"m-toc-anchor\"><\/span>Transversal Lines<\/h3>\n<p>\nA line that crosses two lines in a plane at two distinct points is called a transversal line. Transversal lines in combination with special angle relationships are used to determine whether lines in a plane are parallel. <br \/>\n<img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/image_332.png\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<hr>\n<p>\nAs you can see, it is essential to understand the relationships between the \u201cundefined\u201d terms of a point, a line and a plane in order to strengthen and expand your understanding of <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/volume-and-surface-area-of-a-cube\/\">other geometry concepts<\/a>. It\u2019s important to review these frequently from the ground up to keep pace and to retain your knowledge.<\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are lines?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>In the context of mathematics, a line is an infinitely long collection of points. A line has no width or depth*, and it will continue to run in opposite directions forever. We designate that something is a line by marking arrows on both (visible) ends of a line segment.<br \/>*Because a line only has length as a dimension, it is a 1-dimensional object.<\/p>\n<p>This:<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106692 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-1.png\" alt=\"short line segment\" width=\"345\" height=\"82\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-1.png 615w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-1-300x71.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><br \/>would not necessarily be considered a line in a math course because we don\u2019t know if this object has specific endpoints or if it runs on forever. <\/p>\n<p>However, we can turn this into a line by strategically placing 2 arrows:<br \/><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-106677 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-2.png\" alt=\"line with arrows on either end\" width=\"294\" height=\"75\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-2.png 511w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-2-300x76.png 300w\" sizes=\"auto, (max-width: 294px) 100vw, 294px\" \/><br \/>As you might guess, a line never has a visible \u2018ending.\u2019 In fact, a line doesn\u2019t have <em>any<\/em> ending because it is <em>infinitely<\/em> long!<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you define a point?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>A point is a set position (or \u201ccoordinate\u201d) within a space. Traditionally, a point is designated by a simple \u2018dot\u2019 on some surface; and it\u2019s either named by a single letter and\/or described in \\((x,y)\\)&#8211; or \\((x,y,z)\\)-coordinate form.<\/p>\n<p>Remember that a point is a dimensionless object because it doesn\u2019t have any width, length, or depth.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106689 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-3.png\" alt=\"on the left is point G, on the right is a coordinate graph with the point (2, 3) plotted and labeled\" width=\"458\" height=\"237\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-3.png 942w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-3-300x155.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-3-768x397.png 768w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/> <\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is a collinear point?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Collinear points are points that sit on the same line, line segment, or ray.<br \/>The points A, B, and C are collinear.<br \/><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-106686 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-4.png\" alt=\"line with points A, B, and C\" width=\"198\" height=\"209\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-4.png 464w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-4-283x300.png 283w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><br \/>The points X and Y are <em>not<\/em> collinear because Y isn\u2019t on the same line as X.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-106683 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-5.png\" alt=\"line with point X in the middle and point Y to the right, off of the line\" width=\"194\" height=\"197\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-5.png 458w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-5-295x300.png 295w\" sizes=\"auto, (max-width: 194px) 100vw, 194px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is a plane in math?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Think of a plane as the surface of an ever-lasting piece of paper: a flat surface that you can only move up and down or right and left on. You couldn\u2019t move \u201cin\u201d or \u201cout.\u201d <br \/><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-106680 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-6.png\" alt=\"parallelogram, dashed line going through the middle in both directions, vertical and horizontal\" width=\"348\" height=\"264\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-6.png 703w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-6-300x228.png 300w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><br \/>A plane is the collection of an infinite amount of points and lines, and it has both length and width (but no depth). Hence, a plane has only 2 dimensions.<\/p>\n<p>We usually call it \u2018the \\(xy\\)-plane,\u2019 because we describe points and lines in relation to the horizontal axis, \\(x\\), and the vertical axis, \\(y\\).<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106698 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-7.png\" alt=\"coordinate graph with x-axis and y-axis labeled\" width=\"421\" height=\"265\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-7.png 835w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-7-300x189.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-7-768x483.png 768w\" sizes=\"auto, (max-width: 421px) 100vw, 421px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you identify a plane?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>There are a few different ways to identify\/construct a plane:<\/p>\n<ul>\n<li>Using 3 non-collinear points: When looking at a collection of 3 points that don\u2019t sit on a line together, one might notice that the only way to \u201cconnect\u201d the points to one another is to have them sitting on the same plane together.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106695 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-8.png\" alt=\"points on left I, II, and III, arrow pointing to the right, on the right is a parallelogram with points I, II and III in it\" width=\"568\" height=\"167\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-8.png 1623w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-8-300x88.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-8-1024x302.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-8-768x226.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-8-1536x452.png 1536w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/p>\n<li>Using a line and a separate point: This method is very similar to the one outlined above. Imagine that we drew a line connecting 2 out of the 3 points from above; the only way to connect the two new objects would, again, be to draw a plane.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106710 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-9.png\" alt=\"Line D and point Q with a parallelogram around them\" width=\"584\" height=\"178\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-9.png 1563w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-9-300x92.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-9-1024x313.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-9-768x234.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-9-1536x469.png 1536w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><\/p>\n<li>Using a pair of intersecting lines: Imagine that you have two lines that cross over one another at some shared point. There is only one way to sit these lines on the same flat surface, and so we construct a plane that gives the two lines \u2018common ground.\u2019<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-106707 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-10.png\" alt=\"Line N and M intersecting and are surrounded by a parallelogram\" width=\"546\" height=\"178\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-10.png 1580w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-10-300x98.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-10-1024x334.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-10-768x250.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-10-1536x501.png 1536w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/>\n<li>Using a pair of parallel lines: Once again, this is similar to the intersecting lines method we just discussed. There is only one way to set up a plane for these parallel lines to sit on together.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106704 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-11.png\" alt=\"two parallel horizontal lines labeled &quot;Line O&quot; and &quot;line P&quot; with a parallelogram around them\" width=\"556\" height=\"145\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-11.png 1852w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-11-300x78.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-11-1024x267.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-11-768x200.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-11-1536x401.png 1536w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Does a plane always have 3 points?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Technically, yes- a plane always has <em>at least<\/em> 3 points; because a plane is a collection of <em>infinitely-many<\/em> points. However, we can\u2019t identify or construct a plane given less than 3 points.<\/p>\n<p>Let\u2019s say that we\u2019ve been given the point A,<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106701 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-12.png\" alt=\"point labeled &quot;A&quot;\" width=\"85\" height=\"92\" \/>, and are told to, \u201cfind the unique plane that this point sits on.\u201d Unfortunately, this is an impossible task! The amount of possible planes that we could come up with is <em>endless<\/em>.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106722 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-13.png\" alt=\"rectangles in 3 different directions with point A in the center\" width=\"301\" height=\"217\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-13.png 565w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-13-300x216.png 300w\" sizes=\"auto, (max-width: 301px) 100vw, 301px\" \/><\/p>\n<p>Now let\u2019s say that we\u2019ve been given the points E and F<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106746 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-14.png\" alt=\"point E on the left and point F on the right\" width=\"158\" height=\"134\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-14.png 376w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-14-300x254.png 300w\" sizes=\"auto, (max-width: 158px) 100vw, 158px\" \/><br \/>and told to find the plane (like above). While there\u2019s only 1 unique line that connects this pair, again: we run into the problem that there are infinitely-many possible planes that the two points could be sitting on together.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106743 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-15.png\" alt=\"three rectangles slightly rotated for each one, two points in the middle labeled &quot;E&quot; and &quot;F&quot;\" width=\"251\" height=\"213\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-15.png 548w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-15-300x255.png 300w\" sizes=\"auto, (max-width: 251px) 100vw, 251px\" \/><br \/>When you are given 3 points, you have made certain that the space you are looking at is a plane because there is only one unique plane that all 3 points can lie on <\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Does one line define a plane?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>No, a single line cannot be used to define a unique plane. As mentioned above, 1 line can sit on a countless amount of possible planes.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106740 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-16.png\" alt=\"three rectangles in three different directions with a line going through all of them labeled &quot;line J&quot;\" width=\"278\" height=\"177\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-16.png 684w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-16-300x191.png 300w\" sizes=\"auto, (max-width: 278px) 100vw, 278px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are line segments?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>It might seem silly at first, but a line <em>segment<\/em> is actually quite different from a <em>line<\/em> in math. This distinction is important: while a <em>line<\/em> continues infinitely in both directions, a <em>line segment<\/em> has a finite length. More specifically, line segments run from one \u201cendpoint\u201d to another, and these <em>endpoints<\/em> are the points that sit on both ends of the line segment.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106737 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-17.png\" alt=\"line segment with two points on the end\" width=\"243\" height=\"53\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-17.png 586w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-17-300x66.png 300w\" sizes=\"auto, (max-width: 243px) 100vw, 243px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What does a ray look like in math?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>A ray is kind of like the combination of a line and a line segment; it has 1 endpoint, but on the opposite end it continues on forever.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106734 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-18.png\" alt=\"ray with a point on the left and an arrowhead on the right\" width=\"247\" height=\"54\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-18.png 586w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-18-300x66.png 300w\" sizes=\"auto, (max-width: 247px) 100vw, 247px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the difference between intersecting lines and perpendicular lines?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>While 2 lines are considered <em>intersecting lines<\/em> if they cross over one another at a particular point, they are only considered <em>perpendicular<\/em> to one another if all 4 angles formed at the intersection point are <em>right angles<\/em> (each measures 90\u00b0).<\/p>\n<p>Keep in mind: all perpendicular lines are intersecting lines, but not all intersecting lines are perpendicular.<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106731 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-19.png\" alt=\"2 intersecting lines and 2 perpendicular lines\" width=\"484\" height=\"230\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-19.png 1359w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-19-300x143.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-19-1024x487.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-19-768x365.png 768w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/p>\n<p text-align: center;> The lines A and B are simply intersecting. However, the lines C and D are perpendicular.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are parallel and intersecting lines?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>There are only 2 possible relationships that a pair of lines can have between themselves: they are either parallel or they are intersecting (or will eventually intersect) one another. <\/p>\n<p>If it\u2019s impossible for 2 lines to ever cross over one another, they are considered parallel. If the lines cross over one another at some point (we call this point the \u201cintersection point\u201d), we call them \u201cintersecting lines.\u201d<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106728 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-20.png\" alt=\"group of parallel lines and a group that will eventually intersect\" width=\"491\" height=\"188\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-20.png 1477w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-20-300x115.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-20-1024x392.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-20-768x294.png 768w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/p>\n<p text-align: center;> The lines K and L are parallel to one another; and while K\u2019 and L\u2019 are not yet intersecting, they will eventually meet at the intersection point to the right.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you identify a transversal line?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>A transversal line is one which intersects at least 2 other lines. In the following figures, the dashed line is the transversal:<br \/><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-106725 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-21.png\" alt=\"different groups of lines with a dotted line that intersects them\" width=\"472\" height=\"229\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-21.png 1828w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-21-300x146.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-21-1024x497.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-21-768x373.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Lines-and-Planes-FAQ-21-1536x745.png 1536w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Lines_and_Planes_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Lines and Planes Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nA ________ is a part of a line that has one fixed starting point, and extends infinitely in one direction. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Midpoint<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">Ray<\/div><div class=\"PQ\"  id=\"PQ-1-3\">Line Segment<\/div><div class=\"PQ\"  id=\"PQ-1-4\">Transversal<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A <strong>ray<\/strong> is a part of a line that has one fixed starting point, and extends infinitely in one direction.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70874 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Example-of-a-Ray.png\" alt=\"Example of a Ray\" width=\"277\" height=\"99\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Example-of-a-Ray.png 823w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Example-of-a-Ray-300x107.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Example-of-a-Ray-768x274.png 768w\" sizes=\"auto, (max-width: 277px) 100vw, 277px\" \/><\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nName the plane in the image below.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70871 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Plane-with-points-EFG-and-a-T.png\" alt=\"Plane with points EFG and a T\" width=\"339\" height=\"195\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Plane-with-points-EFG-and-a-T.png 701w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Plane-with-points-EFG-and-a-T-300x172.png 300w\" sizes=\"auto, (max-width: 339px) 100vw, 339px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">Plane EF<\/div><div class=\"PQ\"  id=\"PQ-2-2\">Shape <em>T<\/em><\/div><div class=\"PQ\"  id=\"PQ-2-3\">Plane G<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">Plane EFG or Plane <em>T<\/em><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A plane can be named by an italicized letter such as <em>T<\/em>, or by three non-collinear points that lie on the plane, such as EFG.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich capital letters in the alphabet have parallel lines.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70868 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/picture-showing-the-alphabet.png\" alt=\"picture showing the alphabet\" width=\"341\" height=\"209\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/picture-showing-the-alphabet.png 1070w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/picture-showing-the-alphabet-300x184.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/picture-showing-the-alphabet-1024x630.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/picture-showing-the-alphabet-768x472.png 768w\" sizes=\"auto, (max-width: 341px) 100vw, 341px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">E, F, H, M, N, X, Y, and Z <\/div><div class=\"PQ\"  id=\"PQ-3-2\">E, F, H and M <\/div><div class=\"PQ\"  id=\"PQ-3-3\">E, H, M, N, and Z <\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">E, F, H, M, N, W, and Z <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Parallel lines will never cross each other even when extended infinitely. The letters E, F, H, M, N, W, and Z consist of parallel lines.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich geometric term best describes how the city of Austin, Texas would be represented on a globe? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">Line<\/div><div class=\"PQ\"  id=\"PQ-4-2\">Plane<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">Point<\/div><div class=\"PQ\"  id=\"PQ-4-4\">Ray<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A point describes a location, such as Austin, Texas on a globe. In geometry, a point does not take up space, but in pictures or diagrams they are drawn as dots.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nAndrew wants to build a model of a skyscraper using paper. He decides to design the building as a triangular prism. How many planes will be used to create this model? <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-70862 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/paper-model-of-a-triangular-pyramid-skyscraper.png\" alt=\"paper model of a triangular pyramid skyscraper\" width=\"112\" height=\"272\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/paper-model-of-a-triangular-pyramid-skyscraper.png 297w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/paper-model-of-a-triangular-pyramid-skyscraper-123x300.png 123w\" sizes=\"auto, (max-width: 112px) 100vw, 112px\" \/> <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">Three planes<\/div><div class=\"PQ\"  id=\"PQ-5-2\">Four planes<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">Five planes<\/div><div class=\"PQ\"  id=\"PQ-5-4\">Six planes<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The model will be built from five planes: top, bottom, and three sides.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":91729,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-57940","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-shape-videos","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/57940","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=57940"}],"version-history":[{"count":8,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/57940\/revisions"}],"predecessor-version":[{"id":279319,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/57940\/revisions\/279319"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91729"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=57940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}