Question

An isosceles trapezoid is a quadrilateral with two congruent legs and a pair of parallel bases. Prove the base angles of an isosceles trapezoid are congruent. Be sure to create and name appropriate geometric figures.

Answer 1

Check the picture below.

now, we know that the slanted legs are congruent, since it's an isosceles trapezoid, we also know that the bases are the parallel sides, so, the "altitude" or distance from those bases are the same length, for each of those triangles in the picture.

now, the bases are parallel, that means the altitude segment is perpendicular to the base, the longest side at the bottom, so, we end up with a right-triangle that has a Hypotenuse and a Leg, equal to the other triangle's.

thus, by the HL theorem for right triangles, both of those triangles are congruent, and if the triangles are congruent, all their sides are also, including the ones on the base.