Question

A kite is a quadrilateral with two pairs of adjacent, congruent sides. Prove the two angles between the non-congruent sides are congruent. Be sure to create and name the appropriate geometric figures.

Answer 1

Given: Polygon ABCD is a kite with \(\overline{\rm AD} \cong \overline{\rm AB}\) and \(\overline{\rm CD} \cong \overline{\rm CB}\).
Prove: \(\angle D \cong \angle B\)

Answer 2

Draw a segment connecting points A and C.
Then you have the two sets of congruent sides that are given.
Side \(\overline{\rm AC} \) is congruent to itslef.
By SSS you can prove that \(\triangle ADC \cong \triangle ABD\).
Then by CPCTC, \(\angle D \cong \angle B\).