Question

Important for my exam tomorrow ! Please help

Answer 1

Explanation:

Adjacent angles of parallelogram are supplementary.

∠A + ∠D = 180

Divide both sides by 2

`(1)/(2)` ∠A +
`(1)/(2)` ∠D = 90

∠PAD + ∠ADP = 90 --------------------(I)

IN ΔPAD,

∠PAD + ∠ADP + ∠APD = 180 {angle sum property of triangle}

90 + ∠APD = 180 {from (I)}

∠APD = 180 - 90

∠APD = 90

∠SPQ = ∠APD {vertically opposite angles}

∠SPQ = 90°

Similarly, we can prove ∠PQR = 90° ; ∠QRS = 90° and ∠RSP = 90°

In a quadrilateral if each angle is 90°, then it is a rectangle.

PQRS is a rectangle.