Maharashtra State BoardSSC (English Medium) 9th Standard
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In δ Pqr, If Pq > Pr and Bisectors of ∠ Q and ∠ R Intersect at S. Show that Sq > Sr. - Geometry

Sum

In Δ PQR, If PQ > PR and bisectors of ∠ Q and ∠ R intersect at S. Show that SQ > SR.

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Solution

In △PQR, PQ > PR
Now, the angle opposite to the greater side is greater than angle opposite to the smaller side.
∴ ∠R > ∠Q
Dividing both sides by 2, we get

`1/2 angle "R" > 1/2 angle "Q"`

⇒ ∠SRQ > ∠SQR
⇒ SQ > SR       (The sides opposite to the greater angle is greater than side opposite to the smaller angle)
Hence proved.

Concept: Angle bisector theorem
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APPEARS IN

Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 3 Triangles
Problem Set 3 | Q 3 | Page 49
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