The Angle Bisectors of a Parallelogram Form a Rectangle
The Angle Bisectors of a Parallelogram Form a Rectangle
| The Angle Bisectors of a Parallelogram Form a Rectangle : A parallelogram is a quadrilateral in which both the opposite pair of sides are parallel and equal to each other. The angle bisectors of a parallelogram form a rectangle | |
Theorem: The Angle Bisectors of a Parallelogram Form a Rectangle. GIVEN A parallelogram ABCD in which bisectors of angles A, B, C, D intersect at P, Q, R, S to form a quadrilateral PQRS. To Prove PQRS is a rectangle. Proof Since ABCD is a parallelogram. Therefore, AD Now, AD
[ |  |
But, in we have
[Sum of the angles of a triangle is
]
[
are vertically opposite angles
]
Similarly, we can prove that
Hence, PQRS is a rectangle.
ILLUSTRATION: LMOP is a quadrilateral in which LM = OP and and
. The angle bisectors of LMOP form a quadrilateral ABCD. Find the measure of
Solution: In the quadrilateral LMOP But they are cointerior angles when LM and PO are two straight lines and LP is the transversal As they are supplementary. LM || PO Also LM = PO [ Given]
As we know that the angle bisectors of a parallelogram form a rectangle.
Hence |  |
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