Question

ABCD is a quadrilateral such that diagonal AC bisects the angles ∠ A and ∠ C. Prove that AB = AD and CB = CD.

Answer 1

By considering △ ABC and △ ADC

We know that AC bisects at ∠ A

So we get

∠ BAC = ∠ DAC

We know that AC is common i.e. AC = AC

From the figure we know that AC bisects at ∠ C

∠ BCA = ∠ DCA

By ASA congruence criterion we get

△ ABC ≅ △ ADC

Therefore, it is proved that AB = AD and CB = CD (c. p. c. t)