Trapezoids and Kites
It’s important when working with quadrilaterals to know their different traits. First, let’s look at two different trapezoids we have here. In both these trapezoids and in all trapezoids, all trapezoids have one pair of parallel sides so segment HI is a parallel segment to KJ and segment R-S is parallel to QT. So that one pair of parallel sides is often referred to as the basis and in this first trapezoid we couldn’t make any other conclusions about the diagnoal bisecting each other, being congruent or perpendicular or anything like that. However, with this second trapezoid, QRST, this is called an isoseles trapezoid like an isoseles triangle these two non-parallel sides are congruent and isosceles trapezoid is special because their diagnoal are congruent so diagonal RT is congruent to diagonal QS but again that’s only true in isoseles trapezoids, not all trapezoids. Let’s look at this kite – ABCD – so all kites have two pairs of sides that are congruent and none of their sides are parallel so here segment AB is congruent to segment BC and segment AD is congruent to segment CD and because of this special property of kites then their diagonals are perpendicular so segment BD is perpendicular to segment AC and segment BD bisects segment AC and what that means is that it cuts segment AC into two congruent segments and that is not true of the reverse. Segment AC does not bisect segment BD so hopefully these traits will help you solve some geometry problems.
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Last updated: 07/25/2017
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