Question

35) Prove that the bisectors of any two adjacent angles of a square form an isosceles right angled
triangle​

Answer 1

Hi

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

OB bisects ∠B and OC bisects ∠C

Thus, ∠OBC=∠OBA

∠B=∠OBC+∠OBA=90

Thus, ∠OBC=∠OBA=45

Similarly, ∠OCB=∠OCA=45

Since, ∠OCB=∠OBC=45

△ OBC is an isosceles triangle.

In △OBC,

∠OBC+∠OCB+∠BOC=180 (Sum of angles)

45+45+∠BOC=180

∠BOC=90

Thus, OBC is a right angled isosceles triangle.