Q1 of 42 Page 202

In Δ PQR, ST is a line such that and also ∠PST = ∠PRQ. Prove that ΔPQR, is an isosceles triangle.

Given,


Also, ∠PST = ∠PRQ


⇒ Need to prove that PQR is an isosceles triangle.


⇒ If a line divides any two sides of a triangles in the same ratio then the same line is parallel to the third side.


⇒ Since, ST || QR


⇒ ∠PST = ∠PQR …………eq(1)


(Corresponding angles)


Also given ∠PST = ∠PRQ ……………eq(2)


From eq(1) and eq(2) we get


⇒ ∠PQR = ∠PRQ


Since, sides opposite to equal angles are equal


⇒ PR = PQ


∴ two sides of PQR is equal


PQR is an isosceles triangle


Hence proved.


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