In the given figure- if x-y and A B-C B- then A E is -A- less than CDB- greater than CDC- equal to CD

The correct option is C equal to CDIn Δ ABE and Δ CBD, 1) ∠ x = ∠ y So, 180^∘ ∠ x = 180^∘ ∠ y ∴ nbsp;∠ AEB=∠ CDB 2) AB = CB .... (Given) 3) ∠ CBD = ∠ ABE . ...

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Byju's Answer

Standard VII

Mathematics

Congruency of Triangles

In the given ...

Question

In the given figure, if $x = y$ 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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Solution

The correct option is C equal to CD
In $Δ A B E$ and $Δ C B D$ ,
1) $∠ x = ∠ y$
So, $180^{\circ} - ∠ x = 180^{\circ} - ∠ y$
$∴ ∠ A E B = ∠ C D B$
2) AB = CB .... (Given)
3) $∠ C B D = ∠ A B E$ ..... (Common angle) $∴ Δ A B E ≅ Δ C B D$ ..... (AAS criterion for congruency)
$\Rightarrow$ AE = CD ..... (CPCT).

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

The correct option is C equal to CDIn ΔABE and ΔCBD, 1) ∠x=∠y So, 180∘−∠x=180∘−∠y ∴∠AEB=∠CDB 2) AB = CB .... (Given) 3) ∠CBD=∠ABE ..... (Common angle) ∴ΔABE≅ΔCBD ..... (AAS criterion for congruency) ⇒AE = CD ..... (CPCT).

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