Question

prove that the bisectors of any two consecutive angles of a rectangle are perpendicular to each other

Answer 1

take an angle of 180 degree

divide into 2 at centre point

then if it forms 90 degree then its a perpendicular

Answer 2

ABCD is a parallelogram. OA and OD are the bisectors of adjacent angles,∠A and ∠D.

ABCD is a parallelogram.

∴ AB||DC (Opposite sides of the parallelogram are parallel)

AB||DC and AD is the transversal,

∴ ∠BAD + ∠CDA = 180° (Sum of interior angles on the same side of the transversal is 180°)

1/2BAD +1/2CDA = 1/2 180

⇒ ∠1 + ∠2 = 90° (AO and DO are angle bisectors ∠A and ∠D) ...(1)

In ΔAOD,

∠1 + ∠AOD + ∠2 = 180°

⇒∠AOD + 90° = 180° [from (1)]

⇒∠AOD = 180° – 90° = 90°

∴ In a parallelogram, the bisectors of the adjacent angles intersect at right angle.