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

Let AB and CD are respectively the smallest and largest sides of a quadrilateral ABCD (see figure), then which of the following is true?

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

∠ A > ∠ C and ∠ B < ∠ D

∠ A < ∠ C and ∠ B < ∠ D

∠ A > ∠ C and ∠ B > ∠ D

∠ A < ∠ C and ∠ B > ∠ D

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that AB and CD are respectively the smallest and largest sides of a quadrilateral.
Construction:
Join the points A and C and the points B and D.

AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD. Show that ∠A > ∠C and ∠B > ∠D. - Sarthaks eConnect | Largest Online Education Community

Δ A B C,

We have AB as the smallest side, therefore,

A B < B C

We know that the angle opposite to the greater side is larger.

∴ ∠ A C B < ∠ B A C (1)

Δ A D C,

We have DC as the largest side, therefore,

D C > A D

We know that the angle opposite to the greater side is larger.

∴ ∠ D A C > ∠ A C D (2)

From figure,

∠ D A B = ∠ B A C + ∠ D A C (3)

∠ D C B = ∠ A C B + ∠ A C D (4)

Adding equations (1) and (2), we get,

∠ B A C + ∠ D A C > ∠ A C B + ∠ A C D

⇒ ∠ D A B > ∠ D C B from eq (3) & (4)

⇒ ∠ A > ∠ C

Δ A B D,

We have AB as the smallest side, therefore,

A B < A D

We know that the angle opposite to the greater side is larger.

∴ ∠ A D B < ∠ A B D (5)

Δ B D C,

We have DC as the largest side, therefore,

D C > B C

We know that the angle opposite to the greater side is larger.

∴ ∠ B D C < ∠ D B C (6)

From figure,

∠ A B C = ∠ D B C + ∠ A B D (7)

and

∠ A D C = ∠ A D B + ∠ B D C (8)

Add equation (5) and (7) get,

∠ D B C + ∠ A B D > ∠ A D B + ∠ B D C

⇒ ∠ A B C > ∠ A D C from eq (7) & (8)

⇒ ∠ B > ∠ D

Therefore, if AB and CD are respectively the smallest and largest sides of a quadrilateral
ABCD, then

∠ A > ∠ C and ∠ B > ∠ D .

Hence, option (3) 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!

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

best study material, now at your finger tips!

live classes
progress tracking
24x7 mentored guidance
study plan analysis

download the app

Let AB and CD are respectively the smallest and largest sides of a quadrilateral ABCD (see figure), then which of the following is true?

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App