In figure below, $AB\ ∥\ QR$, find the length of $PB$.

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**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,

$\vartriangle PAB ∠¼ \vartriangle PQR$ (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 $2\ cm$.**