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In figure below, $AB\ ∥\ QR$, find the length of $PB$.
"
Given:
In the given figure $AB\ ∥\ QR$.
To do:
We have to find the length of $PB$.
Solution:
$AB = 3\ cm, QR = 9\ cm$ and $PR = 6\ cm$
In $\vartriangle PAB$ and $\vartriangle PQR$,
$\angle P = \angle P$ (Common)
$\angle PAB = \angle PQR$ ($AB||QR$, Corresponding angles)
Therefore,
$\vartriangle PAB ∼ \vartriangle PQR$ (By AA similarity)
Hence,
$\frac{AB}{QR} = \frac{PB}{PR}$ (Corresponding parts of similar triangles are proportional)
$\frac{3}{9} = \frac{PB}{6}$
$PB = \frac{6}{3}$
$PB = 2\ cm$
The value of $PB$ is $2\ cm$.
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