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Question
In quadrilateral ABCD, AD = BC and BD = CA.
Prove that:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA
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Solution
Given: In quadrilateral ABCD, AD = BC and BD = AC.
To Prove:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA
Proof:
In ΔABD and ΔBAC,
AD = BC ....(given)
BD = CA ....(given)
AB = AB ....(common)
∴ ΔABD ≅ ΔBAC ....(by SSS congruence criterion)
`{:(∠"ADB" = ∠"BCA"), (∠"DAB" = ∠"CBA"):}} ...("c.p.c.t.")`
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