Question

EXERCISE - 8.1
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Give
PS PT
1. In APQR, ST is a line such that and also ZPST = ZPRQ.
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Prove that APQR is an isosceles triangle.
PS PT
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Answer 1

Answer:

Step-by-step explanation:

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.