Question

5. In figure 5.25. if points P, Q, R, S are
on the sides of parallelogram such that
AP = BO = CR
DS then prove that
PORS is a parallelogram.
Fig. 5.25​

Answer 1

Answer:

Given ABCD is a parallelogram so

AD = BC and AD ∥BC

and DC = AB and DC ∥ AB

also AP = BQ = CR = DS

⇒ AS = CQ and PB = DR

in ΔAPS and Δ CRQ

∠ A = ∠C (opposite ∠s of a parallelogram are congruent)

AS = CQ

AP = CR

ΔAPS ≅ Δ CRQ( SAS congruence rule)

⇒ PS = RQ (c.p.c.t.)

Similarly PQ= SR

Since both the pair of opposite sides are equal

PQRS is ∥gram.