ABCD is a quadrilateral such that diagonal AC bisects the angles ∠A and ∠C.

Question:

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

 

 

Solution:

Given: In quadrilateral ABCDAC bisects the angles ∠A and ∠C.

To prove: AB AD and CB CD

Proof:
In ">ΔABC and ">ΔADC,

">BAC = ">DAC            (Given, AC bisects the angles ∠A)
AC = AC                        (Common side)
">BCA = ">DCA            (Given, AC bisects the angles ∠C)

"> By ASA congruence criteria,
">ΔABC ">">ΔADC

Hence, AB AD and CB CD.     (CPCT)

 

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