Question

In a triangle PQR altitude PS bisectors the side PR,Prove that triangle PQR is an isosceles triangle

Answer 1

since it bisects the side PR...
RS=SQ
now consider the 2 triangles:-
triangle PRS and triangle PSQ....
here...
RS=SQ
PS=SP(common side)
and... angle PSR=angle PSQ
hence triangles are congruent by SAS congruence criterion...
therefore by cpct...
angle PRS=angle PQS
sides opposite to equal angles are equal..
therefore in triangle POR.. PR=PQ..
hence it is an isosceles triangle

Answer 2

Answer:

In triangle PSQ and PSR

ANGLE PSQ=PSR

QS=RS

PS=PS

THUS IT IS AN ISOSCELES TRIANGLE

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