Question

□ABCD is a parallelogram, P , Q are midpoint of its opposite sides seg AB and seg DC respectively,. If seg AQ intersects seg DP in R and seg BQ intersects seg CP in S then prove that □PRQS is a parallelogram.​

Answer 1

Answer:

ABCD is ∥gm

AB∥CD

AE∥FC

⇒AB=CD

2

1

AB=

2

1

CD

AE=EC

AECF is ∥gm

In △DQC

F is mid point of DC

FP∥CQ

By converse of mid point theorem P is mid point of DQ

⇒DP=PQ (1)

∴AF and EC bisect BD

In △APB

E is mid point of AB

EQ∥AP

By converse of MPT ( mid point theorem )

Q is mid point of PB

⇒PQ=QB (2)

By (1) and (2)

⇒PQ=QB=DP

AF and EC bisect BD..

Answer 2

Answer:

answer for the given problem is given

Step-by-step explanation:

Using Concept:-

• Opposite sides are parallel and equal.