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Similarity Rules of Triangles: Angle Angle Similarity Theorem

In the given ...

Question

In the given figure, find the length of $Y Z$ .

37

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37.5

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38

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36

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Solution

The correct option is B $37.5$ cm
In triangles $△ A B C$ and $△ X Y Z$

$∠$ $B$ = $∠$ $Y$ (given)
$∠$ $C$ = $∠$ $Z$ (given)
Hence, $△ A B C \sim △ X Y Z$
(by AA property)

So the corresponding sides will be in the same ratio.

$\frac{A B}{X Y} = \frac{B C}{Y Z}$
$\Rightarrow \frac{5}{15} = \frac{12.5}{Y Z}$
$\Rightarrow Y Z = 3 \times 12.5 c m$
$\Rightarrow Y Z = 37.5 c m$

Hence, option $(b)$ correct.

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In the given figure, find the length of YZ.

The correct option is B 37.5 cmIn triangles △ABC and △XYZ ∠ B = ∠ Y (given) ∠ C = ∠ Z (given) Hence, △ABC∼△XYZ (by AA property) So the corresponding sides will be in the same ratio. ABXY=BCYZ ⇒515=12.5YZ ⇒YZ=3×12.5 cm ⇒YZ=37.5 cm Hence, option (b) correct.

In the given figure, find the length of $Y Z$ .