Question

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

Answer 1

R.E.F image

Solution :-

Let BP and CP are bisector of angles B and C respectively

we need to prove that bisectors of the base angles of a triangle can never enclose a right angle.

In $△ABC,\angle A+\angle B+\angle C={180}^{\circ }$

Now $\angle A+2\angle 1+2\angle C={180}^{\circ }$

$2(\angle 1+\angle 2)={180}^{\circ }-\angle A$

$\Rightarrow \angle 1+\angle 2={90}^{\circ }-\frac{\angle A}{2}$

In $△PBC,\angle P+\angle 1+\angle 2={180}^{\circ }$

$\angle P+{90}^{\circ }-\frac{\angle A}{2}={180}^{\circ }$

$\angle P={90}^{\circ }+\frac{\angle A}{2}$

Hence angle P is always greater then ${90}^{\circ }$

Thus $PBC$ can never be a right angled triangle