Question

If AD and PM are median of triangles ABC and PQR respectively such that triangle ABC is similar to triangle PQR .
Prove that AB/PQ =AD/PM​

Answer 1

Step-by-step explanation:

Consider the triangles △ABC and △PQR

AD and PM being the mediums from vertex A and P respectively.

Given : △ABC∼△PQR

To prove : PQAB=PMAD

It is given that △ABC∼△PQR

⇒PQ/AB=QR/BC=PR/AC

[ from the side-ratio property of similar △ s]

⇒∠A=∠P,∠B=∠Q,∠C=∠R.......(A)

BC=2BD;QR=2 QM     [P,M being the mid points of BC q QR respectively]

⇒PQ/AB=2QM/2BD=PR/AC

⇒PQ/AB=QM/BD=PR/AC........(1)

Now in △ABDq△PQM

PQAB=QMBP........[ from (1)]

∠B=∠Q

⇒△ABD∼△PQM [ By SAS property of similar △ s] from the side property of similar △ s Hence proved

PQ/AB=PM/AD