Question

State true or false:

The bisectors of any two adjacent angles of a square form an isosceles-right-angled triangle.

• A. True
• B. False

Answer 1

The correct option is A True

Consider a square ABCD. Bisectors of adjacent angles B and C meet at O.
In a square, all the angles are right angles or ${90}^{\circ }$
OB bisects $\angle B$ and OC bisects $\angle C$
Thus, $\angle OBC=\angle OBA$
$\angle B=\angle OBC+\angle OBA=90$
Thus, $\angle OBC=\angle OBA=45$
Similarly, $\angle OCB=\angle OCA=45$
Since, $\angle OCB=\angle OBC=45$
$△$ OBC is an isosceles triangle.
In $△OBC$,
$\angle OBC+\angle OCB+\angle BOC=180$ (Sum of angles)
$45+45+\angle BOC=180$
$\angle BOC=90$
Thus, OBC is a right angled isosceles triangle.