Q: 5  Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Answers (1)

Given : ABCD is a quadrilateral with  AC=BD,AO=CO,BO=DO,\angleCOD =90 \degree

 To prove: ABCD is a square.

Proof: Since the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a rhombus.

           Thus, AB=BC=CD=DA

           

               In \triangleBAD and \triangleABC,   

                AD=BC              (proved above )

               AB=AB               (common)

               BD=AC

             \triangleBAD \cong \triangleABC   (By SSS)

           \angle BAD = \angle ABC    (CPCT)

            \angleBAD+\angleABC =180 \degree           (Co-interior angles)

                   2. \angleABC = 180 \degree

                         \angleABC =90 \degree 

Hence,  the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions