ABCD is a rectangle in which diagonal AC bisects A as well as C. Show that ABCD is a square.

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Solution

Given ABCD is a rectangle
with $∠ 1 = ∠ 2$ and $∠ 3 = ∠ 4$

But $∠ 1 = ∠ 4$ (alternate angles)
Therefore, we have $∠ 2 = ∠ 4,$ which means $A B = B C,$ similarly $A D = C D$
Hence, ABCD is a square.

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