∠ ABE = ∠ EBD nbsp;= x° (say) nbsp; nbsp;...... nbsp; [Given] nbsp;BE DC nbsp;...... nbsp; [Given] ∠ ABE = ∠ BCD = x° ....... nbsp; [Corres ...

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SSS Criteria for Congruency of Triangles

then BI

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.

$\Rightarrow B D = D C$

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