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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