Question

If the bisectors of angles B and C of a parallelogram ABCD meet in any point on side AD, then prove that BC = 2 AB.​

Answer 1

Answer:

Given: ABCD is a parallelogram. OB and OC bisect ∠B and ∠C, OBC is a right isosceles triangle.

To prove: ABCD is a rectangle

In △OBC,

∠BOC=90

∘

OB=OC

Hence, ∠OBC=∠OCB=x

Sum of angles = 180

∠OBC+∠OCB+∠BOC=180

x+x+90=180

2x=90

x=45

∘

Hence, ∠OBC=∠OCB=45

∘

or ∠B=∠C=90

∘

(OB and OC bisect ∠B and ∠C)

Since, adjacent angles are right angles. ABCD is a rectangle.