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Posted by Diya Lalwani 5 years, 2 months ago
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Sia ? 5 years, 2 months ago
Given: PQ = PR
To prove: PS > PQ
Proof: In {tex}\triangle{/tex}PRQ, we have
PR = PQ [Given]
{tex}\Rightarrow \;\angle 1 = \angle R{/tex}
[{tex}\therefore{/tex} Angles opposite to the equal side of the triangle are equal]
But, {tex}\angle 1 > \angle S{/tex} [{tex}\therefore{/tex} Exterior angle of a triangle is greater than each of the remote interior angles]
{tex} \Rightarrow \;\angle R > \angle S{/tex} {tex}[\because \angle 1 = \angle R]{/tex}
{tex}\Rightarrow{/tex} PS < PR [{tex}\because{/tex} In a triangle, side opposite to the large is longer]
Hence, proved.
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