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....
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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
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