Question

2. In the given figure PR is a diagonal of the parallelogram PQRS.
(i) Is PS = RQ? Why?

(ii) Is SR = PQ? Why?
(iii) Is PR = RP? Why?
(iv) Is ΔPSR ≌ ΔRQP? Why?

Answer 1

Heya,

Answer to your question is:-

Given: PQRS is a ||gm(parallelogram) and PR is one of it's diagonals.

(i.) Yes, PS = RQ because opposite sides of a ||gm are equal.

(ii.) Yes, SR = PQ because opposite sides of a ||gm are equal.

(iii.) Yes, PR=RP because it is a common side.

(iv.) Yes, ∆PSR ≌ ΔRQP because diagonal of a ||gm divides it into two congurent triangles.

HOPE THIS HELPS YOU:-))
@Ashu

Answer 2

Given:

PR is a digonal of the parallelogram PQRS.

To Find:

PS = RQ

SR = PQ

PR = RP

ΔPSR ≅ ΔRQP

Solution:

(i)  PS = RQ is equal because the opposite angles of a parallelogram are equal.

(ii) SR = PQ as they are the opposite angles of the parallelogram.

(iii) PR = RP because they are the opposite sides of the parallelogram.

(iv) ΔPSR ≅ ΔRQP as digonal PR divides the parallelogram into two congruent triangles.