Q34 of 805 Page 257

If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.

Given,

In ΔPQR,


PS bisects ∠QPR and QS = SR


To prove:


PQ = PR



In ΔPQS and ΔPRS


QS = SR [Given]


∠QPS = ∠RPS [Given]


PS = PS [Common]


ΔPQS is congruent to ΔPRS [S.A.S]


⸫ PQ = PR [C.P.C.T.C]


Hence Proved.


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