ABCD is a quadilateral in which AD=BC and angle DAB=angle CBA prove that BD=AC

Step-by-step explanation:

Given data:

ABCD is a quadrilateral.

AD = BC – – – – (1)

∠DAB = ∠CBA – – – – (2)

To prove that BD = AC:

In ΔABD and ΔBAC,

AD = BC (given side)

∠DAB = ∠CBA (given angle)

AB = BA (reflexive side)

Therefore ΔABD ≅ ΔBAC by SAS congruence rule.

By corresponding parts of congruence triangles,

BD = AC

Hence proved.

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step-by-step explanation: