Q3 of 45 Page 49

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

Given:


SQ and SR are bisectors of ∠Q and ∠R which meet at S


PQ > PR


To Prove: SQ > SR


Proof:


PQ > PR


∠PRQ > ∠PQR [angle opposite to longer side is larger] …………(1)


SQ and SR are bisectors of ∠Q and ∠R


∴ ∠SQR = 1/2 ∠PQR and ∠SRQ = 1/2 ∠PRQ


Dividing (1) by 1/2 we get


1/2 ∠PRQ > 1/2 ∠PQR


⇒ ∠SRQ > ∠SQR


⇒ SQ > SR [sides opposite to greater angle is longer]


More from this chapter

All 45 →
1

Choose the correct alternative answer for the following questions.

In ΔTPQ, ∠T = 650, ∠P = 950 which of the following is a true statement?

 2

ΔABC is isosceles in which AB = AC. seg BD and seg CE are medians. Show that BD = CE.

 4

In figure 3.59, point D and E are on side BC of ΔABD, such that BD = CE and AD = AE. Show that ΔABD ≅ ΔACE.

 5

In figure 3.60, point S is any point on side QR of ΔPQR.

Prove that: PQ + QR + RP > 2PS