Question

ABCD is a quadrilateral such that AB = AD and BC = CD prove that the diagonal AC bisects angle A and angle C​

Answer 1

$\huge \mathcal {\fcolorbox{red}{gray}{\green{A}\pink{N}\orange{S}\purple{W}\red{E}\blue{R}{!}}}$

In ΔABC and ΔADC,

∠BAC=∠DAC (given)

∠ACB=∠ACD (given)

AC=AC (common)

∴ΔABC≅ΔADC (ASA axiom)

∴AB=AD and CB=CD by CPCT.

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