Q. 8

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

Answer :

In sum of all angles of a triangle is 180o

A + B + C = 180o


Divide both sides by 2, we get


A + B + C = 180o


A + OBC + OCB = 90o [Therefore, OB, OC bisects B and C]


OBC + OCB = 90o - A


Now, in


BOC + OBC + OCB = 180o


BOC + 90o - A = 180o


BOC = 90o - A


Hence, bisector open base angle cannot enclose right angle.


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