Question

Triangle ABC is similar to triangle PQR. AD is the median to BC and PM is the median to QR.
Prove that AB/PQ = AD/PM

PLEASE HELP ME WITH THIS GUYS....

Answer 1

Answer:

To prove . AB / PQ = AD/ PM

Step-by-step explanation:

proof :- AD is the median

BD = CD =1/2BC

similarly, PM is the median

QM=RM =1/2QR

Now,

∆ABC → ∆PQR.

AB/PQ = BC/ QR = AC/PR

(Corresponding sides of similar triangle are proportional)

So,

AB/PQ =BC/QR

AB/PQ = 2BD/2QM

AB/PQ = BD/QM

Also, since ∆ABC ~ ∆PQR.

(Since AD & PM are medians)

...(1)

/_B=/_Q

(Corresponding angles of similar triangles are equal)

...(2)

NOW,

IN ∆ABD & ∆PQM

/_B= /_Q

AB/PQ= BD/QM

HENCE ,

∆ABD ~∆PQM

SINCE,

AB/PQ = AD/PM

.... PROVED