The bisector of interior angles of a parallelogram forms a rectangle.

# The bisector of interior angles of a parallelogram forms a rectangle.

1. A
PQRS have a measure of  therefore, not  PQRS is a rectangle
2. B
PQRS have a measure of  therefore, PQRS is a rectangle
3. C
PQRS have a measure of  therefore, PQRS is a angle
4. D
PQRS have a measure of  therefore, PQRS is a rectangle

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### Solution:

Let us observe the triangle APB. We know that the opposite sides of a parallelogram are parallel.
Therefore, AC ll BD and AB is the transversal.
Now, angle A + angle (co – interior angles)
Now, in a similar way, AC ll BD and CD is the transversal.
So, by following the same method as shown above, we get the measure of angle R.
R=Now, as we know that AB ll CD, therefore, the transversal is BD.
angle B + angle  (co – interior angles)
Now, in a similar way, AB ll CD and AC is the transversal.
So, by following the same method as shown above, we get the measure of angle S.
Angle S = So,
Angle P = angle R = angle Q = angle S = We have  all the angles of PQRS have a measure of  Therefore, PQRS is a rectangle.
So, option 4 is correct.

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