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Question
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that
- ΔABD ≅ ΔBAC
- BD = AC
- ∠ABD = ∠BAC.
Solution
In quadrilateral ABCD, we have
AD = BC and ∠DAB = ∠CBA
i. In ΔABD and ΔBAC,
AD = BC ...[Given]
∠DAB = ∠CBA ...[Given]
AB = BA ...[Common]
∴ ΔABD ≅ ΔBAC ...[By SAS congruency]
ii. Since ΔABD ≅ ΔBAC
BD = AC ...[By Corresponding parts of congruent triangles]
iii. Since ΔABD ≅ ΔBAC
∠ABD = ∠BAC ...[By Corresponding parts of congruent triangles]
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