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Similar Triangles

ABCD is a qua...

Question

ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA
Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ ABD = ∠ BAC

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Solution

Given,
In ΔABD and ΔBAC,
AD = BC
∠ DAB = ∠ CBA
AB = AB …(common)
(i) ΔABD ≅ ΔBAC by SAS test.
(ii) BD = AC …(CPCT)
(iii) ∠ ABD = ∠ BAC …(CPCT)

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ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that

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(ii) BD = AC

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