Question

diagonal AC of a quadrilateral ABCD bisects angle. if BC=DC prove that AB = AD​

Answer 1

Since diagonal AC bisects the angles ∠A and ∠C,

we have ∠BAC=∠DAC and ∠BCA=∠DCA.

In triangles ABC and ADC,

we have

∠BAC=∠DAC (given);

∠BCA=∠DCA (given);

AC = AC (common side).

So, by ASA postulate, we have

△BAC≅△DAC

⇒ BA = AD and CB = CD (Corresponding parts of congruent triangle).