Question

sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. show that ∆ABC similar to triangle ∆PQR

Answer 1

HEYA!

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Given,  ΔABC where AD is the median and ΔPQR where PM is the median and AB/PQ = BC/QR = AD/PM

RTP - ΔABC ∼ ΔPQR  

Proof:

Since AD is the median

So, BD = CD = BC/2

Similarly, PM is the median

So, QM = RM = QR/2

Again given that  

 AB/PQ = BC/QR = AD/PM

=> AB/PQ = 2BD/2QM = AD/PM

=> AB/PQ = BD/QM = AD/PM    ..............1

Since all 3 sides are proportioanl

So, ΔABC ∼ ΔPQM       {SSS similarity rule}

Hence, ∠B = ∠Q .......2   {Corresponding angles of similar triangles are equal}

In ΔABC and ΔPQR,

∠B = ∠Q               {From equation 2}

AB/PQ = BC/QR    {Given}

Hence by SAS similarity

ΔABC ∼ ΔPQR

Hence proved.

(draw one more triangle similar to ABC)

Answer 2

hope it's help u..........