Question

ABCD is a parallelogram, if P, Q, R and S are the midpoints of the sides AB,BC, CD and DA respectively,
then prove that PQRS is also a parallelogram.​

Answer 1

Answer:

join P,Q,R,S and join BD

in ∆ABD,using mid point theorem,we get,

PS||BD

Using mid point theorem in ∆CDB,we get,

QR||BD

QR||BD and PS||BD

So, QR||PS

Similarly we can prove that SR||PQ

Pair of opposite sides of quadrilateral PQRS are parallel.

So,PQRS is a parallelogram

Hope it helps

Answer 2

Step-by-step explanation:

ABCD is an parallelogram

Join AC

In ∆ABC,

P&Q are mid-points of AB&BC respectively

•PQ II AC

PQ= 1/2 AC (By mid point theorem)--1

ABCD is an parallelogram

Join AC

In ∆ADC,

S&R are mid-points of AD&DC respectively

•SR II AC

SR= 1/2AC ( By mid point theorem)--2

From equation 1 and 2

PQ II AC II SR

•PQ II SR

PQ= 1/2 AC=SR

•PQ=SR

Hope it helps you!