In the given figure, G is the midpoint of the side PQ of ∆PQR and GH || QR. Prove that H is the midpoint of the side PR of the ∆PQR.
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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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