Question

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

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Solution

Given: In quadrilateral ABCD, AC bisects the angles ∠ A and ∠ C. To prove: AB = AD and CB = CD Proof: In ∆ ABC and ∆ ADC, ∠ BAC = ∠ DAC (Given, AC bisects the angles ∠ A) AC = AC (Common side) ∠ BCA = ∠ DCA (Given, AC bisects the angles ∠ C) ∴ By ASA congruence criteria, ∆ ABC ≅∆ ADC Hence, AB = AD and CB = CD . (CPCT)

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