Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

Write the shape of the quadrilateral formed by joining the mid-points of the sides of a rhombus taken in order.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

Rectangle.

Square.

Rhombus.

Parallelogram.

answer is A.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given, a rhombus.
Question Image

Consider ABCD is a rhombus with points P, Q, R and S as mid-points of sides AB, BC, CD, AD respectively.
In

Δ A B C

, P is the mid-point of AB and Q is the mid-point of BC.
By mid-point theorem,

P Q ∥ A C, P Q = 12 A C

… (1)
Similarly,

S R ∥ A C, S R = 12 A C [By midpoint theorem]

… (2)
Thus,

P Q ∥ S R, P Q = S R

[From (1) and (2)]
Thus, PQRS is a parallelogram.
Also, ABQS is a parallelogram.

⇒ A B = S Q

[Opposite sides of parallelogram] … (3)
Similarly, PBCR is a parallelogram.

⇒ B C = P R [Opposite sides of parallelogram] ⇒ A B = P R [AB =BC, Sides of rhombus] ⇒ S Q = P R [From (3)]

So, the diagonals of a parallelogram are equal.
Hence, PQRS is a rectangle.
The quadrilateral is rectangle.
Hence, the correct option is 1.

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test