{"id":71201,"date":"2021-04-08T14:04:10","date_gmt":"2021-04-08T19:04:10","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=71201"},"modified":"2026-03-28T11:23:24","modified_gmt":"2026-03-28T16:23:24","slug":"congruent-angles","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/congruent-angles\/","title":{"rendered":"Congruent Angles"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_nIY2asjDVpo\" 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_nIY2asjDVpo\" data-source-videoID=\"nIY2asjDVpo\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Congruent Angles Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Congruent Angles\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_nIY2asjDVpo:hover {cursor:pointer;} img#videoThumbnailImage_nIY2asjDVpo {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2497-thumb-final-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_nIY2asjDVpo\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_nIY2asjDVpo\" 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\",\"Congruent Angles\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_nIY2asjDVpo\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_nIY2asjDVpo\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_nIY2asjDVpo\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction fF7_Function() {\n  var x = document.getElementById(\"fF7\");\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=\"fF7_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=\"fF7\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Congruent_Angle_Overview\" class=\"smooth-scroll\">Congruent Angle Overview<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Alternate_Interior_Angles\" class=\"smooth-scroll\">Alternate Interior Angles<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Alternate_Exterior_Angles\" class=\"smooth-scroll\">Alternate Exterior Angles<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Corresponding_Angles\" class=\"smooth-scroll\">Corresponding Angles<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Vertical_Angles\" class=\"smooth-scroll\">Vertical Angles<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Triangle_Congruence\" class=\"smooth-scroll\">Triangle Congruence<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Congruent_Angle_Practice_Questions\" class=\"smooth-scroll\">Congruent Angle Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"overview\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"overview\">Overview<\/label><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"overview-spoiler\">\n<h2><span id=\"Congruent_Angle_Overview\" class=\"m-toc-anchor\"><\/span>Congruent Angle Overview<\/h2>\n<p>Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.<\/p>\n<p>There are many rules that allow us to determine whether angles are congruent or not. For example, if two triangles are similar, their corresponding angles will be congruent. This means that the angles that are in the same matching position will have the same angle.<\/p>\n<p>Another common test for angle congruence requires a set of parallel lines and a transversal line that slices through the set of parallel lines. For example, lines a and b are parallel, and line l is a transversal that slices through the parallel lines. When this situation occurs, a handful of congruent angles are formed.<\/p>\n<p>There are four main types of congruent angles formed in this scenario: alternate interior angles, alternate exterior angles, corresponding angles, and vertical angles. <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71231\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"..\/wp-content\/uploads\/2021\/04\/Image-of-parallel-lines-a-and-b-and-a-transversal-line-l.png\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-parallel-lines-a-and-b-and-a-transversal-line-l.png 1234w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-parallel-lines-a-and-b-and-a-transversal-line-l-300x191.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-parallel-lines-a-and-b-and-a-transversal-line-l-1024x651.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-parallel-lines-a-and-b-and-a-transversal-line-l-768x488.png 768w\" alt=\"Image of parallel lines a and b and a transversal line (l)\" width=\"512\" height=\"325\" \/><\/p>\n<h3><span id=\"Alternate_Interior_Angles\" class=\"m-toc-anchor\"><\/span>Alternate Interior Angles<\/h3>\n<p>Alternate interior angles are located in between the two parallel lines but on alternate sides of the transversal. For this particular example, the congruent alternate interior angles would be \u22202 and \u22206, and \u22207 and \u22203.<\/p>\n<h3><span id=\"Alternate_Exterior_Angles\" class=\"m-toc-anchor\"><\/span>Alternate Exterior Angles<\/h3>\n<p>Similarly, alternate exterior angles are located on the outside of the parallel lines, and on alternate sides of the transversal. \u22205 and \u22201 are congruent, as well as \u22204 and \u22208.<\/p>\n<h3><span id=\"Corresponding_Angles\" class=\"m-toc-anchor\"><\/span>Corresponding Angles<\/h3>\n<p>Corresponding angles are located on the same side of the transversal and in a similar matching location. For example, \u22204 and \u22206 are corresponding angles, therefore they are congruent. Other pairs of corresponding angles include \u22203 and \u22205, \u22201 and \u22207, and \u22202 and \u22208.<\/p>\n<h3><span id=\"Vertical_Angles\" class=\"m-toc-anchor\"><\/span>Vertical Angles<\/h3>\n<p>Vertical angles are formed by angles that are opposite of each other. For example, \u22201 and \u22203, \u22207 and \u22205, \u22204 and \u22202, \u22206 and \u22208 are all pairs of congruent angles. Vertical angles, or opposite angles, are commonly used as a proof of congruence.<\/p>\n<h2><span id=\"Triangle_Congruence\" class=\"m-toc-anchor\"><\/span>Triangle Congruence<\/h2>\n<p>Another category of congruent angles revolves around triangle congruence. Triangle congruence rules are used to prove if two triangles are congruent or not. These rules take into consideration the side lengths and angles of triangles in order to determine congruence.<\/p>\n<p>Four criteria are used to determine triangle congruence, and they are conveniently named. For example, <strong>S-S-S<\/strong> refers to two triangles that have all side lengths the same. If this is true, then all the corresponding angle measures will be congruent as well. <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71228\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"..\/wp-content\/uploads\/2021\/04\/Triangle-ABC-and-Triangle-PQR-with-congruent-sides.png\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Triangle-ABC-and-Triangle-PQR-with-congruent-sides.png 941w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Triangle-ABC-and-Triangle-PQR-with-congruent-sides-300x162.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Triangle-ABC-and-Triangle-PQR-with-congruent-sides-768x415.png 768w\" alt=\"Triangle ABC and Triangle PQR with congruent sides\" width=\"496\" height=\"268\" \/> <strong>S-A-S<\/strong> refers to two triangles that have two congruent sides, with one congruent angle in between. If this is true, then all the corresponding angles will be congruent. <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71225\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"..\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-SAS.png\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-SAS.png 1331w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-SAS-300x102.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-SAS-1024x349.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-SAS-768x262.png 768w\" alt=\"Two triangles displaying SAS\" width=\"619\" height=\"211\" \/> Similarly, <strong>A-S-A<\/strong> tells us that two triangles have two congruent angles, with one congruent side length in between. Again, if this is true, then all the corresponding angles will be congruent. <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71222\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"..\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-ASA.png\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-ASA.png 1226w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-ASA-300x111.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-ASA-1024x379.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-ASA-768x284.png 768w\" alt=\"Two triangles displaying ASA\" width=\"618\" height=\"229\" \/> Lastly, <strong>A-A-S<\/strong> refers to two triangles that have two corresponding congruent angles, with a corresponding congruent side length. This tells us that all the corresponding angles will be congruent. <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71219\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"..\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-AAS.png\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-AAS.png 1191w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-AAS-300x93.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-AAS-1024x318.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Two-triangles-displaying-AAS-768x239.png 768w\" alt=\"Two triangles displaying AAS\" width=\"618\" height=\"192\" \/><\/p>\n<div id=\"pqs\">\u00a0<\/div>\n<p>Congruent angles are commonly used in the study of geometry and in many real-world occupations. Construction workers, engineers, builders, and artists use congruent angles on a regular basis. Determining whether angles are congruent is an important skill that helps lay the foundation for the study of geometry.<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Angles are everywhere around us. They are used by engineers, architects, and artists to invent creative solutions to specialized problems and to create beautiful fixtures and works of art. Many times, the angles present in shapes and intersecting lines have relationships with each other that we can use to determine their measure. One such relationship is congruence. <\/p>\n<p>If we say that two angles are <strong>congruent<\/strong>, we mean that they have the same measure in degrees. For example, suppose we build a square room where all the corners are 90\u00b0. Its four corners would all have congruent angles because they are all the same measure.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-1-01.svg\" alt=\"\" width=\"350\" height=\"350\" class=\"aligncenter size-full wp-image-198884\"  role=\"img\" \/><\/p>\n<p>Similarly, we know an isosceles triangle has two angles with the same measure. These two angles are therefore congruent. To denote that some angles are congruent to each other, we usually draw an arc in the angles.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-2-02.svg\" alt=\"\" width=\"216\" height=\"100.8\" class=\"aligncenter size-full wp-image-198908\"  role=\"img\" \/><\/p>\n<p>Congruent angles really start popping up when we observe the intersections of straight lines. For example, if one straight line intersects another as shown, we can see that there are pairs of congruent angles created, opposite to each other. Because both lines are straight, the angles on each side are basically mirrored so that the red angles are congruent, and the blue angles are congruent. We call these angles vertical angles.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-3-03.svg\" alt=\"\" width=\"295.2\" height=\"96\" class=\"aligncenter size-full wp-image-198911\"  role=\"img\" \/><\/p>\n<p>It is also helpful to note that because the lines are straight, two <a class=\"ylist\" href=https:\/\/www.mometrix.com\/academy\/adjacent-angles\/>adjacent angles<\/a> together form a straight angle of 180\u00b0. This property will come in handy when you need to solve for missing angles.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-4-03.svg\" alt=\"\" width=\"295.2\" height=\"117.6\" class=\"aligncenter size-full wp-image-198905\"  role=\"img\" \/><\/p>\n<p>Let\u2019s try an example. If angle \\(A\\) is 40\u00b0, what are the measures of angles \\(B\\), \\(C\\), and \\(D\\)? <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-5-04.svg\" alt=\"\" width=\"292.4\" height=\"183.6\" class=\"aligncenter size-full wp-image-198941\"  role=\"img\" \/><\/p>\n<p>Because the two intersecting lines are both straight, we know that the opposite angles \\(A\\) and \\(C\\) are congruent. Therefore \\(C\\) must be 40\u00b0 as well. Similarly, angles \\(B\\) and \\(D\\) are congruent. Their measures can be determined using the fact that \\(A+B\\) must equal 180\u00b0.<\/p>\n<div class=\"examplesentence\">\\(A+B=180\u00b0\\)<br \/>\n\\(40\u00b0+B=180\u00b0\\)<br \/>\n\\(B=140\u00b0\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo \\(B\\) and \\(D\\) must both have measures of 140\u00b0.<\/p>\n<p>What happens when we observe two parallel lines that are intersected by a third line?<\/p>\n<p>Consider the parallel lines \\(p\\) and \\(q\\), and the transversal line \\(t\\) that cuts across them. We now observe two intersections and a total of eight angles.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-6-04.svg\" alt=\"\" width=\"393.38\" height=\"249.73\" class=\"aligncenter size-full wp-image-198944\"  role=\"img\" \/><\/p>\n<p>A close look at these intersections reveals that they are identical to each other. Because \\(p\\) and \\(q\\) are parallel, their intersections with \\(t\\) form congruent angles. So, not only are angles 1 and 3 congruent, but angles 5 and 7 are also included in this same congruence. Likewise, angles 2, 4, 6, and 8 are all congruent.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-7-04.svg\" alt=\"\" width=\"393.38\" height=\"249.73\" class=\"aligncenter size-full wp-image-198947\"  role=\"img\" \/><\/p>\n<p>There are four classifications for the types of congruent angles present in this scenario: vertical angles, corresponding angles, alternate exterior angles, and alternate interior angles.<\/p>\n<p><strong>Vertical angles<\/strong> are those which are opposite each other at a single intersection point. This is like we observed in the earlier example. Here, we see that angles 1 and 3 are again congruent, and because they are opposite each other at the same intersection, they are classified as vertical angles. Similarly, the pairs of angles 2 and 4, 5 and 7, and 6 and 8 are all vertical angle pairs.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-8-04.svg\" alt=\"\" width=\"393.38\" height=\"249.73\" class=\"aligncenter size-full wp-image-198950\"  role=\"img\" \/><\/p>\n<p><strong>Corresponding angles<\/strong> are pairs of angles in the same relative position of the intersection of each parallel line and transversal. Corresponding angles are congruent to each other. For example, angles 2 and 6 are corresponding angles because they both appear to the right of t and above the parallel lines. So, they are congruent angles. Other pairs of corresponding angles in this example are angles 1 and 5, 3 and 7, and 4 and 8.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-9-04.svg\" alt=\"\" width=\"393.38\" height=\"249.73\" class=\"aligncenter size-full wp-image-198953\"  role=\"img\" \/><\/p>\n<p><strong>Alternate exterior angles<\/strong> are pairs of angles that appear on the outsides of the parallel lines and on opposite sides of the transversal. Alternate exterior angles are congruent to each other. Angles 1 and 7 are alternate exterior angles and are therefore congruent to each other. Angles 2 and 8 are also alternate exterior angles, making them congruent to each other.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-10-04.svg\" alt=\"\" width=\"393.38\" height=\"249.73\" class=\"aligncenter size-full wp-image-198956\"  role=\"img\" \/><\/p>\n<p>Similarly, <strong>alternate interior angles<\/strong> are pairs of angles which appear on the inside of the parallel lines and on opposite sides of the transversal. Alternate interior angles are congruent to each other. Here, that would be the pairs 3 and 5, and 4 and 6.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/congruent-angles-11-04.svg\" alt=\"\" width=\"393.38\" height=\"249.73\" class=\"aligncenter size-full wp-image-198938\"  role=\"img\" \/><\/p>\n<p>We\u2019ve discussed that two or more angles are congruent if they share the same angle measure and we have looked at a few geometric applications of congruent angles. These ideas help builders, carpenters, and engineers ensure perfection in their work as they design tools, objects, and buildings. Take some time to work through some example problems on your own, and you\u2019ll soon be seeing congruent angles in the world all around you!<\/p>\n<p>I hope this video was helpful. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Congruent_Angle_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Congruent Angle 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 \/>\nAngles 1 and 2 are corresponding angles. If the measure of Angle 2 is 67\u00b0, what is the measure of Angle 1?<\/p>\n<p><img decoding=\"async\" class=\" wp-image-71216 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-line-with-angles-1-and-2-labeled.png\" alt=\"2 parallel lines with a transversal line with angles 1 and 2 labeled\" width=\"311.15\" height=\"106.05\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-line-with-angles-1-and-2-labeled.png 889w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-line-with-angles-1-and-2-labeled-300x285.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-line-with-angles-1-and-2-labeled-768x731.png 768w\" sizes=\"(max-width: 889px) 100vw, 889px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">164\u00b0 <\/div><div class=\"PQ\"  id=\"PQ-1-2\">24\u00b0<\/div><div class=\"PQ\"  id=\"PQ-1-3\">344\u00b0 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">67\u00b0<\/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>When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners, will be congruent. Angles 1 and 2 are congruent angles, so both have an angle measure of 67\u00b0.<\/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 \/>\nLine \\(r\\) is a transversal that crosses through the two parallel lines \\(s\\) and \\(t\\). List all angles that are congruent to Angle 6. <\/p>\n<p><img decoding=\"async\" class=\" wp-image-71213 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-and-8-angles-labeled-1-through-8.png\" alt=\"2 parallel lines with a transversal and 8 angles labeled 1 through 8\" width=\"310.1\" height=\"255.85\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-and-8-angles-labeled-1-through-8.png 886w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-and-8-angles-labeled-1-through-8-300x248.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/2-parallel-lines-with-a-transversal-and-8-angles-labeled-1-through-8-768x634.png 768w\" sizes=\"(max-width: 886px) 100vw, 886px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\u22208, \u22203, and \u22202 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">\u22208, \u22204, and \u22202 <\/div><div class=\"PQ\"  id=\"PQ-2-3\">\u22202 <\/div><div class=\"PQ\"  id=\"PQ-2-4\">\u22201, \u22207, and \u22202 <\/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>\u22208 is congruent to \u22206 because they are vertical angles, or opposite angles.<\/p>\n<p>\u22202 is congruent to \u22206 because they are corresponding angles (same side of the transversal and in matching corners).<\/p>\n<p>\u22204 is congruent to \u22206 because they are alternate interior angles (alternate sides of the transversal, and between the two parallel lines).<\/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 \/>\nIf the following irregular quadrilaterals are congruent, Angle C must be congruent to what other angle? <\/p>\n<p><img decoding=\"async\" class=\" wp-image-71210 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-quadrilateral-ABCD-and-quadrilateral-EFGH.png\" alt=\"Image of quadrilateral ABCD and quadrilateral EFGH\" width=\"315.35\" height=\"213.85\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-quadrilateral-ABCD-and-quadrilateral-EFGH.png 901w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-quadrilateral-ABCD-and-quadrilateral-EFGH-300x203.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-quadrilateral-ABCD-and-quadrilateral-EFGH-768x521.png 768w\" sizes=\"(max-width: 901px) 100vw, 901px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\u2220E <\/div><div class=\"PQ\"  id=\"PQ-3-2\">\u2220F<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\u2220G<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\u2220H<\/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>Corresponding angles are congruent for polygons that are congruent. <\/p>\n<ul>\n<li>\u2220C is congruent to \u2220G<\/li>\n<li>\u2220D is congruent to \u2220H<\/li>\n<li>\u2220A is congruent to \u2220E<\/li>\n<li>\u2220B is congruent to \u2220F<\/li>\n<\/ul>\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 \/>\nThe city of Seattle is building a walking path that crosses over a pair of railroad tracks. The walking path is represented by the transversal t in the image below. The railroad tracks are represented by the parallel lines l and m. If the city wants to have the walking path cross the tracks at a 135\u00b0 angle (Angle 1), what will the values of Angles 2, 3, and 4 be? <\/p>\n<p><img decoding=\"async\" class=\" wp-image-71207 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-walking-path-lying-across-railroad-tracks.png\" alt=\"Image of a walking path lying across railroad tracks\" width=\"315.35\" height=\"213.85\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-walking-path-lying-across-railroad-tracks.png 1267w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-walking-path-lying-across-railroad-tracks-300x196.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-walking-path-lying-across-railroad-tracks-1024x668.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-walking-path-lying-across-railroad-tracks-768x501.png 768w\" sizes=\"(max-width: 1267px) 100vw, 1267px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\u22202 = 45\u00b0 \u22203 = 135\u00b0 \u22204 = 45\u00b0 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">\u22202 = 45\u00b0 \u22203 = 45\u00b0 \u22204 = 135\u00b0 <\/div><div class=\"PQ\"  id=\"PQ-4-3\">\u22202 = 145\u00b0 \u22203 = 45\u00b0 \u22204 = 45\u00b0 <\/div><div class=\"PQ\"  id=\"PQ-4-4\">\u22202 = 180\u00b0 \u22203 = 45\u00b0 \u22204 = 45\u00b0 <\/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>\u22201 and \u22204 are congruent because they are vertical angles. If \u22201 equals 135\u00b0, then \u22202 must be equal to 45\u00b0 because their sum needs to be 180\u00b0 in order to form a straight line. Now that we know \u22202 equals 45\u00b0, we also know that \u22203 equals 45\u00b0 because they are vertical angles.<\/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 \/>\nKelcy has a rectangular garden that she wants to divide equally into two sections diagonally. One section will be for carrots and the other section will be for kale. She separates the garden into two triangular pieces similar to the image below. If the measure of \u2220DCA is 40\u00b0 what is the measure of \u2220CAB? <\/p>\n<p><img decoding=\"async\" class=\" wp-image-71204 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-rectangle-with-a-diagonal-creating-2-triangles.png\" alt=\"Image of a rectangle with a diagonal creating 2 triangles\" width=\"315.35\" height=\"213.85\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-rectangle-with-a-diagonal-creating-2-triangles.png 844w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-rectangle-with-a-diagonal-creating-2-triangles-300x208.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Image-of-a-rectangle-with-a-diagonal-creating-2-triangles-768x531.png 768w\" sizes=\"(max-width: 844px) 100vw, 844px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">20\u00b0 <\/div><div class=\"PQ\"  id=\"PQ-5-2\">30\u00b0 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">40\u00b0 <\/div><div class=\"PQ\"  id=\"PQ-5-4\">50\u00b0 <\/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>If the line AC forms a transversal through the parallel lines DC and AB, then the angles DCA and CAB will be congruent. Angle DCA and Angle CAB form alternate interior angles, so the measure of Angle CAB will be 40\u00b0.<\/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":155201,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-71201","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-angle-videos","7":"page_category-math-advertising-group","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\/71201","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=71201"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/71201\/revisions"}],"predecessor-version":[{"id":280958,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/71201\/revisions\/280958"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/155201"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=71201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}