NCERT solution Class 9 quadrilaterals

NCERT Solutions

Class 9 Maths

Quadrilaterals

NCERT Questions

Ex.8.1 Q.1
Ex.8.1 Q.2
Ex.8.1 Q.3
Ex.8.1 Q.4
Ex.8.1 Q.5
Ex.8.1 Q.6
Ex.8.1 Q.7
Ex.8.1 Q.8
Ex.8.1 Q.9
Ex.8.1 Q.10
Ex.8.1 Q.11
Ex.8.1 Q.12
Ex.8.2 Q.1
Ex.8.2 Q.2
Ex.8.2 Q.3
Ex.8.2 Q.4
Ex.8.2 Q.5
Ex.8.2 Q.6
Ex.8.2 Q.7

Ex.8.1 Q.4

Show that the diagonals of a square are equal and bisect each other at right angles.

Let ABCD be a square. Let the diagonals AC and BD intersect each other at a point O.

To prove that the diagonals of a square are equal and bisect each other at right angles, we have to

prove AC = BD, OA = OC, OB = OD, and ∠AOB = 90⁰.

In ΔABC and ΔDCB,

AB = DC

(Sides of a square are equal to each other)

∠ABC = ∠DCB

(All interior angles are of 90⁰)

BC = CB

(Common side)

So, ΔABC ≅ ΔDCB

(By SAS congruency)

Hence, AC = DB

(By CPCT)

Hence, the diagonals of a square are equal in length.

In ΔAOB and ΔCOD,

∠AOB = ∠COD

(Vertically opposite angles)

∠ABO = ∠CDO

(Alternate interior angles)

AB = CD

(Sides of a square are always equal)

So, ΔAOB ≅ ΔCOD

(By AAS congruence rule)

Hence, AO = CO and OB = OD

(By CPCT)

Hence, the diagonals of a square bisect each other.

In ΔAOB and ΔCOB,

As we had proved that diagonals bisect each other, therefore,

AO = CO

AB = CB

(Sides of a square are equal)

BO = BO

(Common)

So, ΔAOB ≅ ΔCOB

(By SSS congruency)

Hence, ∠AOB = ∠COB

(By CPCT)

However, ∠AOB + ∠COB = 180⁰

(Linear pair)

2∠AOB = 180⁰

∠AOB = 90⁰

Hence, the diagonals of a square bisect each other at right angles.

Video solution:

Quadrilaterals Class 9 Maths NCERT Chapter 8 NCERT Solutions

Solving NCERT textbook questions of Quadrilaterals Class 9 Maths NCERT Chapter 8 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 9 Maths Quadrilaterals, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 9 Maths Quadrilaterals Online Test on LearnoHub.com.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Quadrilaterals Class 9 Maths Notes.
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NCERT solutions of Quadrilaterals Class 9 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 9 Maths Quadrilaterals NCERT solutions.