Question

A kite is a quadrilateral with two pairs of adjacent, congruent sides. Prove the two angles between non-congruent sides are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Answer 1

BA≅BC Given

DA≅DC Given

ΔCBE ≅ ΔABE by SSS

ΔABD ≅ ΔCBD by SSS

∠A ≅ ∠C by CPCTC

∠B ≅ ∠D by CPCTC

Explanation:

Answer 2

Quadrilateral ABCD is a kite AB is congruent to AD -- definition of a kite BC is congruent to DC -- definition of a kite draw a line segment AC AC is congruent to itself -- identity triangle ABC is congruent to triangle ADC -- SSS angle ABC is congruent to ADC QED