Question

In triangle pqr l and m are two points on the base qr such that angle qpl = angle prq and angle rpm = angle rqp. Prove that pq.pq=qr.ql

Answer 1

...............



hope you are satisfied with my answer

Answer 2

Proved below.

Step-by-step explanation:

Given:

Here in triangle pqr, l and m are two points on the base qr.

∠ qpl = ∠ prq and ∠ rpm = ∠ rqp

Now,

In Δ pqr and Δ pql

∠ pqr = ∠ pql       [ common angle ]

pq = pq                 [ common ]

∠ qpl = ∠ prq       [given]

Hence $\triangle PQR \sim \triangle LQP$  [ By AAS test]

$\frac{qr}{pq}= \frac{pq}{lq}$

$pq \times pq = qr \times ql$

pq · pq = qr · ql

Hence proved.