In figure below, $∠A\ =\ ∠CED$, prove that $ΔCAB\ ∼\ ΔCED$. Also find the value of $x$.
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Given:

In the given figure $∠A\ =\ ∠CED$.

To do:

We have to prove that $ΔCAB\ ∼\ ΔCED$ and find the value of $x$.

Solution:

 In $ΔCAB$ and $ΔCED$,

$\angle C = \angle C$  (Common)

$\angle A = \angle CED$ (given)

Therefore,

$ΔCAB ∼ ΔCED$ (By AA similarity)

This implies,

$\frac{CA}{CE} = \frac{AB}{DE}$  (Corresponding sides are proportional)

$\frac{15}{10} = \frac{9}{x}$

$x = \frac{9\times 10}{15}$

$x=6\ cm$

The value of $x$ is $6\ cm$.

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Updated on: 10-Oct-2022

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