Question

Show that the bisectors of the angles of a parallelogram form a rectangle.
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Answer 1

Step-by-step explanation:

Given : A parallelogram ABCD.

To prove : PQRS is a rectangle.

Proof :

In ΔABS ,

1/2∠A + 1/2∠B + ∠BSA = 180 °

∠A+∠B = 180 ° (Adjacent angles of a parallelogram are supplementary )

∴ 1/2∠A + 1/2∠B = 180 ÷ 2 = 90 °

90 ° + ∠BSA = 180 °

∴ ∠BSA = 180° - 90°

∠BSA = 90°

∠BSA = ∠RSP [Vertically opposite angles ]

∠RSP = 90 °

Similarly , it can be showed that ∠SPQ = 90° , ∠PQR = 90° and ∠QRS = 90°

∴ PQRS is a quadrilateral in which all the angles are of measure 90°.

Hence , PQRS is a rectangle