Maharashtra State BoardSSC (English Medium) 9th Standard
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In the Given Figure, Seg Pt is the Bisector of ∠ Qpr. a Line Through R Intersects Ray Qp at Point S. Prove that Ps = Pr - Geometry


In the given figure, seg PT is the bisector of ∠ QPR. A line through R intersects ray QP at point S. Prove that PS = PR

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According to the figure, we have
PT || SR
If PT || SR and PS is a transversal line, then 
∠ QPT = ∠ PSR   (Corresponding angles)           ....(1)
If PT || SR and PR is a transversal line, then 
∠ TPR = ∠ PRS  (Alternate angles)              ....(2)
We are given that seg PT is the bisector of ∠ QPR.
∴ ∠ QPT = ∠ TPR         ...(3)
From (1), (2) and (3)
∠ PSR = ∠ PRS
The sides opposite to equal angles are also equal in a triangle. 
∴ PS = PR

Concept: Angle bisector theorem
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Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 3 Triangles
Problem Set 3 | Q 7 | Page 50
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