When both legs of the trapezoid are the same length, we have a special type of quadrilateral called an isosceles trapezoid.Īs you might expect, isosceles trapezoids have congruent legs as well as congruent consecutive angles shared by a base. We already know (thanks to our extensive background in working with parallel lines) that consecutive interior angles are supplementary, so we've proven that consecutive angles in a trapezoid that share the same leg are supplementary. Looking at ∠1 and ∠2, we can see that they are consecutive interior angles. Since only the bases are parallel and the legs are not, we can think of this scenario as two nonparallel transversals cutting across a pair of parallel lines. The other two sides that aren't parallel to each other are called the trapezoid's legs. A trapezoid has two bases, each of which is one of the parallel sides. Like kites with their special diagonals, trapezoids also have parts with special names (although none as strange as the names we have for our parts). Since this has two pairs of parallel lines, and a trapezoid must have only one, this is not a trapezoid. How many pairs of parallel lines do you see? The top and bottom are parallel to each other, as are the two sides. So when trapezoids start their own party after being kicked out of the quadrilateral party, we can be certain that rectangles, squares, and parallelograms will definitely not be on the guest list. They absolutely cannot have two sets of parallel sides. Every once in a while, they might strike up a conversation with a lonesome polygon who happens to wander over, but it never lasts long and they just go back to uncomfortably staring at their feet.Ī trapezoid is a quadrilateral with only one set of parallel sides. While the rest of them have their congruent sides and angles to chitchat about, these quadrilaterals just hang by the snack bar. They're different from the rest of the quadrilaterals, kind of like the socially awkward guest at the quadrilateral party. The last family of quadrilaterals are the outcasts.
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