Three statements are given below:

I. In a parallelogram, the angle bisectors of two adjacent angles enclose a right angle.

II. The angle bisectors of a parallelogram form a rectangle.

III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which one is true?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

I only

II only

I and II

II and III

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

Given 3 statements.
I. In a parallelogram, the angle bisectors of two adjacent angles enclose a right angle.
II. The angle bisectors of a parallelogram form a rectangle.
III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.
As, in a parallelogram the angle bisectors intersect and form a right-angle.
Hence, statement I is true.
The angle bisector forms a rectangle as it also intersects at the right-angle.
The statement II is also correct.
Hence, option 3 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th