Question

parallelos
(Figure 5.24)
Fig. 5.24
4. Prove that quadrilateral formed by the
intersection of angle bisectors of all
angles of a parallelogram is a rectangle.​

Answer 1

Answer:

FIGURE GIVEN

Step-by-step explanation:

Given : ABCD a parallelogram

To Prove : PQRS is a rectangle

DC∣∣AB and DA is a traversal

∴∠A+∠D=180

0

2

1

∠A+

2

1

∠D=90

0

⇒∠SAD+∠SDA=90

0

∴∠ASD=90

0

∴ By concept of vertical angles

∠ASD=∠PSR=90

0

Simillarly we will get

∠PQR=∠QPS=∠QRS=90

0

∴PQRS is a rectangle