AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If APB and CQD are two parallel lines, then write the shape of the quadrilateral formed by the bisectors of $∠ APQ, ∠ BPQ, ∠ CQP, ∠ PQD$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Rectangle

Square

Parallelogram

Rhombus

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given, two parallel lines APB and CQD.
Question Image

Let the bisectors of angle APQ and CQP meet at a point M.
And bisectors of angles BPQ and PQD meet at a point N.
Join PM, MQ, QN and NO.
As,

A P B ∥ C Q D

∠ A P Q = ∠ P Q D [Alternate angles with PQ as transversal] ⇒ 2 ∠ M P Q = 2 ∠ N Q P [MP and NQ are angle bisectors] ⇒ ∠ M P Q = ∠ N Q P

Similarly,

∠ B P Q = ∠ C Q P

[Alternate angles]
So, quadrilateral PMQN is parallelogram.

∠ C Q D = 180 ° [Linear angle] ⇒ ∠ C Q P + ∠ D Q P = 180 ° ⇒ 2 ∠ M Q P + 2 ∠ N Q P = 180 ° ⇒ ∠ M Q P = 90 °

Thus, PMQN is a rectangle.
Hence, the correct option is 1.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!