Question

in a triangle PQR,G is the midpoint on side PQ and GH is parallel to QR then prove that H is The midpoint of side PR

Answer 1

Answer:

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Answer 2

Given : G is the midpoint of the side PQ of ∆PQR and GH || QR.

To Find : Prove that H is the midpoint of the side PR of the ∆PQR. ​

Solution:

GH || QR

Equal corresponding angles

∠G = ∠Q

∠H = ∠R

∠P = ∠P  common

Hence

ΔPGH ≈ ΔPQR

Ratio of corresponding side of similar triangle is same

=> PG /PQ  =  PH/PR

G is the midpoint of the side PQ

=> PG = PQ/2

=> PG/PQ = 1/2

=> 1/2 = PH/PR

=> PH = PR/2

Hence H is mid point of PR.

QED

Hence proved

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