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# NCERT Solutions for Class 7 Maths Chapter 7 – Congruence of Triangles

NCERT Solutions for Class 7 Maths Chapter 7 is about the geometrical concept of congruence. In this chapter, there are only 2 exercises and a total of 14 questions. This is a short chapter. The chapter of NCERT Solutions for Class 7 Maths covers the congruence of plane figures, line segments, angles, and triangles.

Try these Solutions for Class 7 Chapter 7 ‘Congruence of Triangles’ which are based on the latest syllabus approved by CBSE. At Instasolv, we provide the most reliable study material for Class 7 Maths. Chapter-wise Solutions of NCERT Class 7 Maths Book are also provided. Instasolv helps you in understanding the concepts better and to score higher marks in the exams.

Chapter 7 Congruence of Triangles, of CBSE NCERT Class 7 Maths Book covers congruence in detail starting from the congruence of plane figures to that of line segments, angles, and triangles. Special focus is given on the congruence of right-angled triangles. We already studied in Chapter 6 the Pythagoras property of a right-angled triangle and its importance. For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. We follow the same sequence as in the book so that it becomes easy to understand and use as a reference.

## NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles: Exercise Discussion

The chapter consists of a total 2 exercises, which are based on the topics discussed below. Read each topic in order to score well in CBSE Class 7 Maths exam.

1.  Introduction – When two objects are exact copies of each other or both have the same shape and size, they are said to be congruent. The relation of two objects being congruent is called congruence. This chapter focuses completely on the geometrical concept of congruence.
2. Congruence of Plain Figures – The method of superimposition can be used. For example, place one stamp over another. The stamp will completely cover the one below if they are of the same shape and size. The stamps will then be called congruent.
3. Congruence of Line SegmentsIf two line segments have the same length they are congruent. Conversely, if two line segments are congruent then they would have the same length.
4. Congruence of AnglesIf two angles have the same measure they are congruent. Conversely, if two angles are congruent then they would have the same measure.
1. Congruence of Triangles

Taking forward the same concept of congruence that we have studied so far, if two triangles are exact copies of each other then they are congruent. If you superimpose one congruent triangle over another then it will completely cover the other one.

There are three sides, angles, and vertices of a triangle. For two triangles to be congruent they must be exact copies. So, for every vertex of one triangle, there must be a corresponding vertex in the other triangle. Similarly, for every angle of one triangle, there must be a corresponding angle of the same measure in the congruent triangle. Also, for every side of one triangle, there must be a corresponding side of the same length in the congruent triangle

1. Criteria for Congruence of Triangles

SSS Congruence Criterion: Under a given correspondence, if the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

SAS Congruence Criterion: Under a correspondence, if two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.

ASA Congruence Criterion: Under a correspondence, if two angles and the included side of a triangle are equal to two corresponding angles and the included side of another triangle, then the triangles are congruent.

1. Congruence Among Right-Angled Triangles

Knowing that the triangles are right-angled, one angle in both the triangles has to be ninety degrees so there is always one angle in these triangles whose measures are the same.

This makes the congruence of right-angled triangles easier. Note that the criterion for right angles triangles will be less only because we are not mentioning the common right angle in both the triangles.

RHS Congruence Criterion: Under a correspondence, if the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent.

## Study Tips for NCERT Class 7 Maths  Chapter 4: Simple Equations

As a student, you aim to get a high score in the exams. Instasolv recommends that you read chapter 7 Congruence of Triangles of CBSE NCERT textbook for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part. This summary can be used as a ready reference. It will also help in improving your clarity about the geometric concept of congruence.

The Pythagoras property was studied at the end of the last chapter. This chapter also ends with the congruence of the right-angled triangle. This is another reiteration of the importance of this topic.

If any concept is still not understood, ask the experts on the Instasolv app which does not charge any student for this support.

1. Do all the exercises, solved examples and self-practice questions on your own before you cross-check from the solutions or ask the experts on the Instasolv app.