Q is a point on the side SR of a triange PSR such that PQ=PR prove that PS is greater than PQ

Q is a point on the side SR of a triange PSR such that PQ=PR prove tha

1.	Q is a point on the side SR of a triange PSR such that PQ=PR prove that PS is greater than PQ
Answer» Given: PQ = PRTo prove: PS > PQProof: In {tex}\\triangle{/tex}PRQ, we havePR = 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}\xa0{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.