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Question
ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD.
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Solution
Given: In a quadrilateral ABCD, diagonal AC bisects the angles A and C.
To prove: AB = AD and CB = CD
Proof: In ΔADC and ΔABC,
∠DAC = ∠BAC ...[∵ AC is the bisector of ∠A and ∠C]
∠DCA = ∠BCA ...[∵ AC is the bisector of ∠A and ∠C]
And AC = AC ...[Common side]
∴ ΔADC ≅ ΔABC ...[By ASA congruence rule]
AD = AB ...[By CPCT]
And CD = CB ...[By CPCT]
Hence proved.
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