Question

show that the bisectors of angles of a parallelogram form a rectangle

Answer 1

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

Answer 2

Answer:

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

Step-by-step explanation: