Question

In a ∆ABC, P and Q are points on sides AB and AC respectively, such that PQ || BC. If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find the AB and PQ.

Answer 1

It is given that ,, and .

We have to find AB and .

So (by Thales theorem)

Then

Now

Since PQ$\parallel$BC, AB is a transversal, then
∠APQ = ∠ABC (corresponding angles)

Since PQ$\parallel$BC, AC is a transversal, then
∠AQP = ∠ACB (corresponding angles)

In ∆APQ and ∆ABC,

∠APQ = ∠ABC (proved above)

∠AQP = ∠ACB (proved above)

so, ∆ APQ ∼ ∆ ABC (Angle Angle Similarity)

Since the corresponding sides of similar triangles are proportional, then

$\frac{\mathrm{AP}}{\mathrm{AB}}=\frac{\mathrm{PQ}}{\mathrm{BC}}=\frac{\mathrm{AQ}}{\mathrm{AC}}$

$$\begin{gathered} \frac{\mathrm{AP}}{\mathrm{AB}}=\frac{\mathrm{PQ}}{\mathrm{BC}} \\ \frac{2.4}{6}=\frac{\mathrm{PQ}}{6} \\ \mathrm{so},\mathrm{PQ}=2.4\mathrm{cm} \end{gathered}$$