Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

In given fig, PR > PQ and PS bisects QPR. Prove that PSR >

Question

In given fig, $PR > PQ$ and $PS$ bisects $∠ QPR$ . Prove that $∠ PSR > ∠ PSQ$ .

Views: 1,106 students

Found 4 tutors discussing this question

Henry Discussed

In given fig,

PR > PQ

and

PS

bisects

∠ QPR

. Prove that

∠ PSR > ∠ PSQ

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Δ PQR

PR > PQ

(Given)

\Rightarrow ∠ PQR > ∠ PRQ

...(1)

(Angle opposite to side of greater length is greater

PS

is the bisector of

∠ P,

∠ x = ∠ y

Adding

∠ x

in (1)

\Rightarrow ∠ PQR + ∠ x > ∠ PRQ + ∠ x

\Rightarrow ∠ PQR + ∠ x > ∠ PRQ + ∠ y

.... (2)

Δ PQS

∠ PQS + ∠ x + ∠ PSQ = 18 0^{\circ}

(Angle sum property of triangle)

∴ ∠ PQS + ∠ x = 18 0^{\circ} - ∠ PSQ

..... (3)

Δ PSR

∠ PRS + ∠ y + ∠ PSR = 18 0^{\circ}

(Angle sum property of triangle)

∠ PRS + ∠ y = 18 0^{\circ} - ∠ PSR

Using equation (1), (2), (3) we get

18 0^{\circ} -∠ PSQ > 18 0^{\circ} - ∠ PSR

...(4)

\Rightarrow - ∠ PSQ > - ∠ PSR

\Rightarrow ∠ PSQ < ∠ PSR

So,

∠ PSR > ∠ PSQ

[h e n ce p ro v e d]

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	In given fig, $PR > PQ$ and $PS$ bisects $∠ QPR$ . Prove that $∠ PSR > ∠ PSQ$ .
Answer Type	Text solution:1
Upvotes	150

In given fig, PR>PQ and PS bisects ∠QPR. Prove that ∠PSR>∠PSQ.

Text solutionVerified

Practice questions from similar books

In given fig, $PR > PQ$ and $PS$ bisects $∠ QPR$ . Prove that $∠ PSR > ∠ PSQ$ .