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MasterElodin
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

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