Question

In a triangle PQR, L and M are two points on the base
QR such that angle LPQ = angle QRP and
angle RPM = angle RQP. Prove that :
(i) triangle PQL is similar to triangle RPM
(ii) QL.RM = PL.PM
(iii) PQ² = QP.QL​

Answer 1

Answer:

Step-by-step explanation:

∠QPL=∠PRM

∠RPM=∠PQL

ΔPQL≈ΔRPM          {AA}

QL/PM=PL/RM        {BPT}

OL×RM=PL×PM

∵ PQ/QP=QL/PQ

 PQ²=QP×QL