In the adjoining figure, AB = CD and AD = BC. Show that $∠ 1 = ∠ 2$

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Solution

In triangles $A B D$ and $C D B,$

We have
$A B = C D$ (Given)
$A D = B C$ (Given)
$B D = D B$ (common side)

Hence, $△ A B D ≅ △ C D B$ , by $SSS$ postulate.

Comparing the angles of the congruent triangles

we get $∠ A D B = ∠ C B D$

$∴ ∠ 1 = ∠ 2$

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