Question

prove that the bisector of any two consecutive angle of a parallelogram intersect at right angles ​

Answer 1

Step-by-step explanation:

prove that the bisector of any two consecutive angle of a parallelogram intersect at right angles

Answer 2

Step-by-step explanation:

Let ABCD is a parallelogram

as we know

∠A+∠B=180

0

OAbisects∠DAB&OBbisects∠CBA

toprove∠AOB=90

0

nowinΔAOB

∠OAB+∠CBA+∠AOB=180

0

2

1

∠DAB+

2

1

∠CBA+∠AOB=180

0

2

1

(∠DAB+CBA)+∠AOB=180

0

2

1

×180

0

+∠AOB=180

0

90

0

+∠AOB=180

0

∠AOB=180

0

−90

0

∠AOB=90

0

Therefore we can say the bisector of any two consecutive angles intersect at the right angle. Hence proved. Note: A property of that parallelogram says that if a parallelogram has all sides equal, then their diagonal bisector intersects perpendicularly.