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.12

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that:

(1) ∠A = ∠B

(2) ∠C = ∠D

(3) ∆ABC ≅ ∆BAD

(4) diagonal AC = diagonal BD

[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

Let us extend AB. Then, draw a line through C, which is parallel to AD, intersecting AE at point

E. It is clear that AECD is a parallelogram.

(1) AD = CE

(Opposite sides of parallelogram AECD)

However, AD = BC

(Given)

Therefore, BC = CE

Hence, ∠CEB = ∠CBE

(Angle opposite to equal sides are also equal)

Consider parallel lines AD and CE.

AE is the transversal line for them.

∠A + ∠CEB = 180⁰

(Angles on the same side of transversal)

∠A + ∠CBE = 180⁰

(Using the relation ∠CEB = ∠CBE) .............(1)

However, ∠B + ∠CBE = 180⁰

(Linear pair angles) ................(2)

From equations (1) and (2), we obtain

∠A = ∠B

(2) AB || CD

∠A + ∠D = 180⁰

(Angles on the same side of the transversal)

Also, ∠C + ∠B = 180⁰

(Angles on the same side of the transversal)

=> ∠A + ∠D = ∠C + ∠B

However, ∠A = ∠B

[Using the result obtained in (1)]

=> ∠C = ∠D

(3) In ∆ABC and ∆BAD,

AB = BA

(Common side)

BC = AD

(Given)

∠B = ∠A

(Proved before)

So, ∆ABC ≅ ∆BAD

(SAS congruence rule)

(4) We have observed that,

∆ABC ≅ ∆BAD.

So, AC = BD

(By CPCT)

Video solution:

Quadrilaterals Class 9 Maths NCERT Chapter 8 NCERT Solutions

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Using the NCERT solutions module effectively can significantly enhance your learning experience and understanding of the subject matter. Here's a step-by-step guide on how to make the most out of the NCERT solutions:

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.
Match with Our Solution: After attempting the question, compare your result and approach with the provided NCERT solution. This step allows you to identify any mistakes or gaps in your understanding.
Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Quadrilaterals Class 9 Maths NCERT Chapter 8 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
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.
Ask for Clarification: If you encounter any doubts or have questions about the solutions, don't hesitate to seek clarification on the “Ask Questions” section of LearnoHub.com. Quadrilaterals Class 9 Maths NCERT Chapter 8 Questions.

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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.