In parallelogram ABCD , AC is diagonal bisect with BD on point O.
NOW,
In triangle AOB and COB, OB is bisect AC
angle AOB. = angle COB
AC = 180. ( linear pair)
Angle AOB + angle COB =. 180
2 ( AOB ). =. 180
angle AOB. = 180/2
angle AOB. =. 90
therefore,
angle AOB + angle COB = 90

Proof that the angle bisectors of a parallelogram intersect at 90 degrees:

Introduction:
A parallelogram is a quadrilateral with opposite sides that are parallel. In this proof, we will show that the angle bisectors of a parallelogram intersect at a right angle, or 90 degrees.

Proof:
Let's assume we have a parallelogram ABCD.

Step 1: Angle Bisectors:
The angle bisectors are the lines that divide the angles of the parallelogram into two equal parts. Let's consider angle B and angle C. The angle bisectors of these angles will be represented by lines BE and CF, respectively.

Step 2: Properties of Parallelogram:
In a parallelogram, opposite sides are parallel and congruent, and opposite angles are also congruent. Therefore, we have the following properties:

- AB || CD (opposite sides are parallel)
- AB = CD (opposite sides are congruent)
- ∠A = ∠C and ∠B = ∠D (opposite angles are congruent)

Step 3: Using Alternate Interior Angles:
Since AB || CD, we can use the property of alternate interior angles. The alternate interior angles formed by the transversal line BC are ∠B and ∠C.

Step 4: Angle Bisector Property:
By definition, angle bisectors divide the angles into two equal parts. Therefore, we have:

- ∠EBF = ∠FBC/2 (angle bisector of ∠B)
- ∠DCF = ∠DCB/2 (angle bisector of ∠C)

Step 5: Proving the Right Angle:
To prove that the angle bisectors intersect at a right angle, we need to show that ∠EBF and ∠DCF are complementary angles, meaning their sum is 90 degrees.

Using the angle bisector property from step 4, we can rewrite the angles as:

- ∠EBF = ∠FBC/2
- ∠DCF = ∠DCB/2

Since ∠FBC and ∠DCB are congruent (opposite angles of a parallelogram), we can substitute them:

- ∠EBF = ∠FBC/2 = ∠DCB/2 = ∠DCF

Now, we have:

- ∠EBF = ∠DCF

Since these angles are equal, they form a linear pair with ∠BCD. Therefore, their sum is 180 degrees:

- ∠EBF + ∠BCD + ∠DCF = 180 degrees

Substituting the equal angles:

- ∠EBF + ∠BCD + ∠EBF = 180 degrees

Simplifying:

- 2∠EBF + ∠BCD = 180 degrees

Since ∠EBF and ∠DCF are equal, we can substitute:

- 2∠EBF + ∠BCD = 180 degrees
- 2∠EBF + ∠EBF = 180 degrees
- 3∠EBF = 180 degrees
- ∠EBF = 60 degrees

Now, we can find the measure of ∠