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Classification of Triangles Based on Sides

In the figure...

Question

In the figure shown, if $B E ∥ D C a n d ∠ E B D = ∠ E B A$ , then BD = ___.

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Solution

$∠ A B E = ∠ E B D$ = x° (say) ...... [Given]

$B E ∥ D C$ ...... [Given]

$∠ A B E = ∠ B C D$ = x° ....... [Corresponding angles]

$∠ E B D = ∠ B D C$ = x° ....... [Alternate angles]

$\Rightarrow Δ B D C$ is an isosceles triangle.

$\Rightarrow B D = B C$

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