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

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PQRS have a measure of

therefore, not PQRS is a rectangle

PQRS have a measure of

therefore, PQRS is a rectangle

PQRS have a measure of

therefore, PQRS is a angle

PQRS have a measure of

therefore, PQRS is a rectangle

answer is D.

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Detailed 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)
Question Image

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

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