Question

Sides AB and AC and median, AD of a triangle. ABC are respectively proportional to sides PQ and QR and median PM of another triangle PQR. Show that triangle ABC similar triangle PQR.

Answer 1

Given, ΔABC where AD is the median and ΔPQR where PM is the median

and AB/PQ = BC/QR = AD/PM

We have to prove that: 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.

Answer 2

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