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

Choose whether given statement is true or false:

If ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Then the angles of the rhombus are $60 °, 120 °, 60 °, 120 °$ .

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

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Drawing rhombus ABCD:
Question Image

Given that, ABCD is a rhombus in which DE is a perpendicular bisector of AB. Also Joining BD.
In

Δ A E D

and

Δ B E D

A E = E B E D = E D ∠ A E D = ∠ D E B = 90 °

Δ A E D ≅ Δ B E D

by SAS rule.

A D = D B = A B

(By C.P.C.T)
So.

Δ A D B

is an equilateral triangle with

∠ D A B = ∠ D B A = ∠ A D B = 60 °

.
Since opposite angles is equal in rhombus then,

∴ ∠ D A B = ∠ D C B = 60 °

Also, in a rhombus adjacent angles of a rhombus are supplementary.

∠ D A B + ∠ A B C = 180 ° ⇒ 60 ° + ∠ A B D + ∠ D B C = 180 ° ⇒ 60 ° + 60 ° + ∠ D B C = 180 ° ⇒ ∠ D B C = 180 ° − 120 ° = 60 °

∠ A B C = ∠ A B D + ∠ D B C = 60 ° + 60 ° ⇒ ∠ A B C = 120 °

As the opposite angles of rhombus are equal.

∴ ∠ A D C = 120 °

Thus, the statement is true.
Hence, option 1 is correct.

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!