In the given figure- if - x - y and AB - CB- then AE isA- equal to CDB- data insufficientC- less than CDD- greater than CD

The correct option is A equal to CDConsider Δ ABE and Δ CBD. Given, ∠ x = ∠ y. 180^∘ ∠ x = 180^∘ ∠ y ∠ CDB = nbsp;∠ AEB Now, AB = CB nbsp; nbsp;(gi ...

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Byju's Answer

Standard IX

Mathematics

AAS Criteria for Congruency

In the given ...

Question

In the given figure, if $\angle x = \angle y$ and AB = CB, then AE is _____.

less than CD

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greater than CD

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equal to CD

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data insufficient

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Solution

The correct option is C equal to CD
Consider $Δ A B E$ and $Δ C B D$ .
Given, $∠ x = ∠ y$ .
$⟹$ $180^{\circ} - ∠ x = 180^{\circ} - ∠ y$
$⟹ ∠ C D B = ∠ A E B$
Now, AB = CB (given) and
$∠ C B D = ∠ A B E$ $(∵$ common angles in $Δ A B E$ and $Δ C B D$ )
Hence, $Δ A B E ≅ Δ C B D$
(by AAS criteria of congruency for triangles)
$∴$ AE = CD (CPCT)

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In the given figure, if \(\angle x = \angle y\) and AB = CB, then AE is _____.

The correct option is C equal to CDConsider ΔABE and ΔCBD. Given, ∠x=∠y. ⟹ 180∘−∠x=180∘−∠y ⟹∠CDB=∠AEB Now, AB = CB (given) and ∠CBD=∠ABE (∵ common angles in ΔABE and ΔCBD) Hence, ΔABE≅ΔCBD (by AAS criteria of congruency for triangles) ∴ AE = CD (CPCT)