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Converse of Basic Proportionality Theorem

In Fig. 7.137...

Question

In Fig. 7.137, AB || QR. Find the length of PB.

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Solution

In $Δ$ PAB and $Δ$ PQR $Δ$
$∠$ APB = $∠$ QPR (common angle)
$∠$ PAB= $∠$ PQR ( corresponding angles)
$∠$ PBA = $∠$ PRQ (corresponding angles)

Hence, $Δ$ PAB and $Δ$ PQR are similar by AAA criteria.
So, $fraction numerator A B over denominator Q R end fraction equals fraction numerator P A over denominator P Q end fraction equals fraction numerator P B over denominator P R end fraction$ ( Corresponding angles of similar triangles)
$3 over 9 equals fraction numerator P B over denominator 6 end fraction P B space equals 2 space c m$

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Similar questions

∥

△ P Q R, A B ∥ Q B

A B

3 c m, P B

2 c m

P R

6 c m

Q R

A B

Q R

\frac{P A}{A Q} = \frac{P B}{B R}

P B = 2

E C = 4

Q R = 9

A B

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