Question 5 If Q is a point on the side SR of a - PSR such that PQ - PR- then prove that PS gt- PQ-

Given in Δ PSR , Q is a point on the side SR such that PQ = PR. To prove PS gt; PQ Proof in Δ PRQ PQ =PR [given] ⇒∠ R =∠ RQR ...(i) [angles opposite to equ ...

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Standard VII

Mathematics

Angles

Question 5 If...

Question

Question 5
If Q is a point on the side SR of a $Δ P S R$ such that PQ = PR, then prove that PS > PQ.

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Solution

Given in $Δ P S R, Q$ is a point on the side SR such that PQ = PR.
To prove PS > PQ

Proof in $Δ P R Q P Q = P R$ [given]
$\Rightarrow ∠ R = ∠ R Q R . . . (i)$
[angles opposite to equal sides are equal]
But $∠ P Q R > ∠ S$ ....(ii)
[exterior angle of a triangle is greater than each of the opposite interior angle]
from Eqs. (i) and (ii) $∠ R > ∠ S$
$\Rightarrow P S > P R$ [side opposite to greater angle is longer]
$\Rightarrow P S > P Q [∵ P Q = P R]$

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Question 5 If Q is a point on the side SR of a ΔPSR such that PQ = PR, then prove that PS > PQ.

Question 5
If Q is a point on the side SR of a $Δ P S R$ such that PQ = PR, then prove that PS > PQ.