NCERT Solutions Class 7 Maths Chapter 7: Congruence of Triangles Exercise 7.3

The exercise in NCERT Solutions Class 7 Maths Chapter 7: Congruence of Triangles, Exercise 7.3 takes you to a deeper level of geometric proof. This exercise presents you with the last set of rules to show that two triangles are exact copies of each other - the ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) Congruence Rules.

As you practice with these exercise problems, you'll recognise that you don't need to know all six pieces (three sides, three angles) of two triangles to prove congruence. If you know both angles and one side, in that order, you have enough information. This knowledge continues to build your ability to create geometric proofs, using only necessary statements and reasons.

1.0Download Class 7 Maths Chapter 7 Ex 7.3 NCERT Solutions PDF

Strengthen your understanding of geometric proofs! Download the in-depth, step-by-step NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.3! This PDF is excellent for reviewing congruence theorems and honing your skills of rigorous proof writing.

2.0Key Concepts of Exercise 7.3 Class 7 Chapter 7 Solutions

• ASA Congruence Theorem: If two angles and the associated side (the side in the middle of those two angles) of one triangle are the same as the two angles and the corresponding side of another triangle, the two triangles are congruent (△ABC≅△XYZ). 
• AAS Congruence Theorem (implicit): Even though we often don't explicitly identify AAS, many problems involve determining the third angle using the Angle Sum Property, so we may conclude that two angles and a non-included side can also prove congruence. 
• CPCT (corresponding parts of congruent triangles): We can then apply this rule to show that parts (sides or angles) of triangles are equal once we have shown all parts of the triangles are equal. This will most often be the last step in a proof in this exercise.
• Recognising Criteria: Problems asking you to recognise which criteria (ASA or AAS) prove a certain pair of triangles are congruent.
• Completing Proofs: Problems needing you to give the missing corresponding parts to prove ASA or AAS.
• Formal Proofs: Answering multi-step problems that involve proving a single pair of triangles congruent, then using CPCT to prove a second pair of triangles or to prove specific sides/angles congruent.

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

4.0Detailed CBSE Class 7 Chapter 7 Exercise 7.3 Solutions

1. Which of the following lengths can be the side lengths of a triangle? Explain your answers. Note that for each set, the three lengths have the same unit of measure.

(i) 2,2,5

(ii) 3,4,6

(iii) 2,4,8

(iv) 5,5,8

(v) 10,20,25

(vi) 10,20,35

(vii) 24,26,28

Sol. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

(i) Here, 2+2<5

So, a triangle cannot be formed.

(ii) Here, 3+4>6,

4+6>3 and 3+6>4

So, a triangle is possible.

(iii) Here, 2+4<8

So, a triangle cannot be formed.

(iv) Here, 5+5>8 and 5+8>5

So, a triangle is possible.

(v) Here, 10+20>25

20+25>10 and 10+25>20

So, a triangle is possible.

(vi) Here, 10+20<35

So, a triangle cannot be formed.

(vii) Here, 24+26>28 and 24+28>26

So, a triangle is possible. 26+28>24

5.0Key Features and Benefits: Class 7 Maths Chapter 7 Exercise 7.3

• Clear Cutting Logical Rigour: Prepares you to always note the least conditions needed for congruence and write proofs with correct justification. 
• Distinguishes Criteria: Clearly differentiates between the SAS, SSS, and angle-based criteria (ASA/AAS).
• Theorems Foundation: Using the congruence rules and CPCT will eventually lead to proving more complex theorems studied later in geometry.