Question

A kite is a quadrilateral with two pairs of adjacent, congruent sides prove that the two angles between the non-congruent sides are congruent

Answer 1

Let us say we have a kite ABCD
with AB = BC
and
CD = DA

If we draw a diagonal across BD, we have two triangles
triangle BCD
and
triangle BAD

Since
AB = BC
and
CD = DA
and
BD = BD (identity property)

triangle BCD = triangle BAD (by SSS postulate)

By virtue of CPCTC, we can prove that
angle B = angle D and
angle C = angle A