NCERT Solutions Class 7 Maths Chapter 7: Congruence of Triangles Exercise 7.6

The concluding stretch of NCERT Solutions Class 7 Maths Chapter 7: Congruence of Triangles takes the form of an expansive review disguised as a possible Exercise 7.6. The goal of this final exercise is to challenge the student to differentiate between all four congruence statements (SSS,SAS,ASA, and RHS), usually in two-dimensional figures that are not simple triangles and to think about how these two-dimensional congruence properties apply to real life in non-standard figures. 

The overarching goal is to develop strong reasoning skills: to look at what is drawn in a figure, to decide which congruence statement applies, and to write a short but reasonable proof to demonstrate congruence or a derived property of a shape (using CPCT). 

1.0Download Class 7 Maths Chapter 7 Ex 7.6 NCERT Solutions PDF

Make sure you've studied the whole chapter! Download step-by-step NCERT Solutions for Class 7 for a complete practice set that covers all congruence criteria. This PDF is the perfect last-minute recap and consolidation of the concept.

2.0Key Concepts of Exercise 7.6 Class 7 Chapter 7 - Congruence of Triangles

• Criterion Selection: The key skill is to quickly find the three equi-part identified and choose the correct criterion from SSS, SAS, ASA or RHS. 
• Proof Justification: Giving the correct reason for all steps including such properties as: 

Common Sides/Angles

Vertically Opposite Angles

Given Conditions

CPCT

• Geometric Problem Solving: Application of congruence to prove properties of quadrilaterals, altitudes, medians and bisectors inside triangles.
• Mixed Criteria Questions: Questions for which the relevant criterion shifts from part one to part two. 
• Proving Higher-Level Properties: Questions that ask to show that a line segment is a bisector using congruency or that a pair of angles/sides are equal within a larger figure. 
• Conceptual Check: Questions that essentially re-test whether AAA and ASS are valid congruence rules.

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

4.0Detailed NCERT Solutions for Class 7 Chapter 7 Exercise 7.6 Solutions

1. Construct triangles for the following measurements.

(i) 75∘,5 cm,75∘

(ii) 25∘,3 cm,60∘

(iii) 120∘,6 cm,30∘

Sol. (i) 75∘,5 cm,75∘

The steps of construction are given as

(a) Draw a line segment AB of length 5 cm using a ruler and a pencil.

(b) Draw angles of 75∘ and 75∘ at points A and B respectively using protector.

(c) Let these two rays intersect at point C .

Then, △ABC is the required triangle.

(ii) 25∘,3 cm,60∘

The steps of construction are given as

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

(b) Draw angles of 25∘ and 60∘ at points A and B respectively using protector.

(c) Let these two rays intersect at point C .

Then, △ABC is the required triangle.

(iii) 120∘,6 cm,30∘

The steps of construction are given as

(a) Draw a line segment AB of length 6 cm using a ruler and a pencil.

(b) Draw angles of 120∘ and 30∘ at points A and B respectively using protector.

(c) Let these two rays intersect at point C .

Then, △ABC is the required triangle.

5.0 Key Features and Benefits: Class 7 Maths Chapter 7 Exercise 7.6

• Final Skills Integration: Combines all geometric notions and congruence criteria studied in this chapter.
• Proof Practice: Focuses on examining intricate figures and articulating rationale at every step is very important in high school geometry.
• Comparison of Concepts: Helps avoid misconceptions or cross differentiation of concepts such as SAS and ASS or RHS with hypotenuses.