NCERT Solutions Class 7 Maths Chapter 7: Congruence of Triangles Exercise 7.5

The NCERT Solutions Class 7 Maths Chapter 7: Congruence of Triangles wraps up by providing you with a last summary and application exercise called Exercise 7.5. This exercise will require you to provide a comprehensive understanding of all four congruence criteria: SSS, SAS, ASA and RHS.

The problems in this exercise could be application exercises, which will require you to systematically analyze geometric figures, select an appropriate criterion to prove congruence, and then make use of CPCT (corresponding parts of congruent triangles) to discover other properties or results. This will ensure you are confident in your application of these fundamental geometric tools in a variety of proof-writing situation.

1.0Download Class 7 Maths Chapter 7 Ex 7.5 NCERT Solutions PDF

Examine your understanding of all the congruence rules! Download the comprehensive, step-wise NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.5. This document is a great resource for your last chapter revision ahead of an exam.

2.0Key Concepts of Exercise 7.5 Class 7 Chapter 7 Congruence of Triangles 

• Holistic Use of Congruence Criteria: Recognising when to employ: 

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)/ AAS (Angle-Angle-Side)

RHS (Right angle - Hypotenuse - Side)

• CPCT as a Proof Tool: Continuously using the rule that corresponding parts of congruent triangles are equal to prove that other sides or angles are equal in a more complex figure. 
• Proof Justification: Presenting clear and straightforward reasons (Given, Common, Proved or a specific Congruence Rule) for every step in a formal proof.
• Varied Congruence Problems: Problems with various given conditions based on which the student is to choose the correct congruence theorem. 
• Complicated Geometric Proofs: Problems that usually have two sets of triangles, and it is necessary to prove the first set to satisfy the conditions (by CPCT) of proving the other set. 
• Real-life Examples of Congruence: Revisiting the idea of congruence and using examples or scenarios that might occur in the "real world" stressing the identical shapes and sizes.

3.0NCERT Solutions Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines : Other Exercises

4.0Detailed CBSE Class 7 Chapter 7 Exercise 7.5 Solutions

1. Construct triangles for the following measurements where the angle is included between the sides.

(i) 3 cm,75∘,7 cm

(ii) 6 cm,25∘,3 cm

(iii) 3 cm,120∘,8 cm

Sol. (i) 3 cm,75∘,7 cm

The steps of construction are given as

(a) Draw a line segment AB of length 7 cm using a ruler and a pencil.

(b) At point A , a draw an angle of 75∘ using protector and mark X .

(c) At point A , mark a point C along A X such that AC=3 cm.

(d) Join the point C to B . Then, △ABC is the required triangle.

(ii) 6 cm,25∘,3 cm

The steps of construction are given as

(a) Draw a line segment AB of length 3 cm using a ruler and a pencil.

(b) At point A , draw an angle of 25∘ using protector and mark X .

(c) At point A , mark a point C along A X such that AC=6 cm.

(d) Join the point C to B . Then, △ABC is the required triangle.

(iii) 3 cm,120∘,8 cm

The steps of construction are given as

(a) Draw a line segment AB of length 8 cm using a ruler and a pencil.

A↪8 cm⟶ B

(b) At point A , draw an angle of 120∘ using protector and mark X .

A120∘X cm​​B

(c) At point A , mark a point C along A X such that AC=3 cm.

(d) Join the point C to B . Then, △ABC is the required triangle.

5.0 Key Features and Benefits: Class 7 Maths Chapter 7 Exercise 7.5

• Overall Assessment: Functions as an excellent assessment to verify that all chapter concepts have been remembered and can be swapped freely.
• Logical Differentiation: Forces students to think critically about the information presented and pick the necessary condition (SSS, SAS, ASA, RHS) as opposed to applying one without thought.
• Deep Conceptual Understanding: Features difficult questions that distinguish between Congruence (an exact copy) and Similarity (same shape, different size) especially with respect to the AAA condition.