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# NCERT Solutions for Class 7 Maths Chapter 7 - Congruence Of Triangles

Last updated date: 05th Aug 2024
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## NCERT Solutions for Class 7 Maths Chapter 7: Complete Resource on Congruence of Triangles - FREE PDF Download

In NCERT Solutions for Class 7 Maths Chapter 7, Congruence of Triangles study material, you will learn the complete concept of congruence of triangles. Other concepts that are covered under this topic are congruence of plane figures, triangles, and the criteria of congruence. Every NCERT Solutions is provided to make the study simple and interesting on Vedantu. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 7 Science , Maths solutions and solutions of other subjects.

 Class: NCERT Solutions for Class 7 Subject: Class 7 Maths Chapter Name: Chapter 7 - Congruence Of Triangles Content-Type: Text, Videos, Images and PDF Format Academic Year: 2024-25 Medium: English and Hindi Available Materials: Chapter WiseExercise Wise Other Materials Important QuestionsRevision Notes

### Class 7 Maths Chapter 7 Includes:

 Chapter 7 Congruence of Triangles All Exercises in PDF Format Exercise 7.1 4 Question and Solutions Exercise 7.2 10 Questions and Solutions

### Facts

• When two line segments have equal lengths then they are called Congruent.

• When the measures of two angles are equal then the angles are called Congruent.

• Two triangles are congruent if the three sides of the one triangle are equal respectively to the three corresponding sides of the other. This rule is called SSS congruence criterion.

• Two angles and the side included between them in one triangle are equal respectively to the corresponding two angles and the included side of another triangle. This rule is called the ASA congruence criterion.

• Two triangles are congruent if two angles and the included angle between them in one of the triangles are equal to the corresponding sides and the included angle of the other triangle. This rule is called the SAS congruence criterion.

• Two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other right triangle. This rule is called RHS congruence criterion.

To solve Exercise 7.1 of NCERT Solutions for Class 7 Chapter 7, you need to understand the facts given below.

Line Segment

The shortest distance between two points is called a line segment.

Angle

Two rays having the same vertex form an angle.

Measure

The opening between the arms of an angle is called its measure.

### Some Facts of Angles

• Vertically opposite angles are equal.

• If the sum of two adjacent angles is 1800, then they are said to form a linear pair.

• When two parallel lines are intersected by a transversal, then alternate angles are equal and corresponding angles are equal.

• The sum of interior opposite angles on the same side of the transversal is 1800.

• In a right-angles triangle, the square of the hypotenuse is equal to the sum of squares of its legs.

### Congruence of Plane Figures

When a plane figure covers the other exactly, then they are said to be of the same shape and same size. Such objects are said to be congruent. Congruent objects are exact replicas of each other. The relationship between two congruent objects is called Congruence.

When two figures are congruent to each other then we write their relationship as Fig.1, Fig.2. (Fig. is referred to as a figure).

Note: Two congruent objects are always similar but two similar figures need not be congruent.

For Example:

• Any two squares are similar but they are congruent only if they have the same length.

• Any two circles are always similar but they are congruent only if they have the same radius.

• Any two equilateral triangles are the same but they are congruent only if their side lengths are the same.

Note:

1. If any two line segments have the same length, then they are congruent. Also if two line segments are congruent, they are said to have the same length.

2. Any two angles having the same measure are congruent. Also, when two angles are congruent, their measures are the same.

3. The congruence of angles entirely depends on the equality of their measures.

4. Two congruent line segments $\overline{AB}$ and $\overline{CD}$ re-written as $\overline{AB}$ ≅ $\overline{CD}$.

5. Two congruent angles ∠ABC and ∠PQR are written as ∠ABC ≅∠PQR.

### Congruence of Triangles

Two triangles are congruent if they are copies of each other and when superimposed, they cover each other exactly.

Suppose,  1st triangle is ΔABC and the 2nd triangle is ΔPQR, we can write ΔABC ≅ ΔPQR.

Since, congruent means “equal in all respects”, a triangle is said to be congruent to another triangle when both the triangles are identical or equal in all respects. In other words, if one figure is placed on the other, they should coincide with each other exactly to be called congruent to one another.

Thus, a triangle is said to be congruent to another if and only if all the six elements (three sides and three angles) of one triangle are respectively equal to the corresponding six elements of the other.

In ΔABC ≅ ΔPQR, the correspondence is:

B ↔P but B does not match (or correspond) Q or R

C ↔ Q but C does not match (or correspond) P or R

D ↔R but D does not match (or correspond) P or Q

(The symbol ↔ means to match or correspond)

Thus,

$\overline{BC} = \overline{PQ}$

$\overline{CD} = \overline{QR}$

$\overline{DB} = \overline{RP}$

and

∠B =  ∠P

∠C = ∠Q

∠D = ∠R

The above order is important. Thus, the triangles BCD and PQR are congruent under the correspondence BCD ↔ PQR.

To understand Exercise 7.2 in NCERT Solutions for Class 7 chapter 7, you need to understand the criteria for congruence of triangles.

### Criteria For Congruence Of Triangles

So far you have learned that for two triangles to be congruent, six parts of one triangle should necessarily be congruent to the six corresponding parts of the other triangle. Now, you will study the rules of congruence, which will help you to understand that two triangles are congruent if three pairs of particular corresponding parts are congruent. The four rules of congruence as follows:

1. Side - Side - Side [SSS]   (Three sides).

2. Side - Angle - Side [SAS]   (Two sides and included angle).

3. Angle - Side - Angle [ASA]   (Two angles and included side).

4. Right Angle - Hypotenuse - Side [RHS]   (Hypotenuse and one side of a right triangle).

## Why Use the NCERT Solutions Provided by Vedantu?

Key Features of NCERT Solutions, These solutions are designed to help students achieve proficiency in their studies. They are crafted by experienced educators who excel in teaching Class 7 Math. Some of the features include:

• Comprehensive explanations for each exercise and questions, promoting a deeper understanding of the subject.

• Clear and structured presentation for easy understanding.

• Accurate answers aligned with the curriculum, boosting students' confidence in their knowledge.

• Visual aids like diagrams and illustrations to simplify complex concepts.

• Additional tips and insights to enhance students' performance.

• Chapter summaries for quick revision.

## Conclusion

NCERT Solutions for Class 7 Maths Chapter 7 - Congruence of Triangles by Vedantu are a valuable resource for students. These solutions provide clear explanations and step-by-step answers to all the questions in the textbook, making it easier for students to understand the concept of congruence in triangles. They help in building a strong foundation in geometry, ensuring that students can solve problems with confidence. The solutions by Vedantu also offer additional practice exercises and tips to enhance problem-solving skills. In simple terms, these solutions are a great support for Class 7 students, ensuring they grasp the concept of congruence in triangles and excel in their math studies.

## FAQs on NCERT Solutions for Class 7 Maths Chapter 7 - Congruence Of Triangles

1. Explain the Properties of Angles.

The properties of angles are:

1. Vertically opposite angles are equal.

2. If the sum of two adjacent angles is 1800, then they are said to form a linear pair.

3. When two parallel lines are intersected by a transversal, then alternate angles are equal and corresponding angles are equal.

4. The sum of interior opposite angles on the same side of the transversal is 1800.

5. In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of its legs.

2. Choose the Correct Answer and Fill in the Blanks:

1. Two angles are said to be congruent, if they have _______________. (equal measures / equal sides)

2. Two plane figures are congruent, if they have_______________. (same shape/ same shape and same size)

3. Two line-segments are congruent, if they are ____________ to each other. (parallel / equal)

1. In Δ P̅Q̅R̅, the side _______________ is included between ∠Q and ∠R.  (PQ / QR)

Solution:

1. Equal measures

2. Same shape and size

3. Equal

1. Q̅R̅

3. Why Should I Opt to Study at Vedantu?

Vedantu has developed a very comprehensive study material for all subjects as per the NCERT syllabus. Experienced teachers and subject-experts are a part of the Vedantu team and they are easily accessible on the Vedantu platform to guide the students with their doubts and a better understanding of the concepts. They help students to develop their foundation and also boost confidence in them. The teachers understand their psychology and interact accordingly. Students learning on Vedantu have shown drastic improvement in their overall performance.

4. Explain the concept of congruence properties of triangles?

Triangles have a lot of crucial qualities, despite how simple their form and understanding appear. Congruence is one of these properties of triangles, which is covered in NCERT Solutions for Class 7. Triangles are congruent. When two objects are stated to be congruent, it simply indicates that they are identical. If the lengths of two line segments are the same, they can be congruent. Angles are no exception to this rule. It can also be similarly applied to triangles. When establishing that two triangles are congruent, there are a few theorems that must be taken into account. In the NCERT Solutions for Chapter 7 of Class 7 Maths, these are logically established and discussed.

5. What all things students will get to know after studying Chapter 7 of Class 7 Maths?

Students will appreciate the usefulness of superposition after going through the fundamental ideas of congruence outlined in this chapter. Superposition is a useful means of assessing whether any two-plane figures are congruent. Students can try applying the congruence requirements for line segments, angles, and triangles to different planar figures after learning about them. Vedantu has all the concepts in the form of pdf. You can download all the solutions and use them for exam purposes from the Vedantu app as well. All the resources are free of cost.

6. What topics are covered in Chapter 7 of Class 7 Maths and how many questions are there?

Starting with the principles of lines, angles, and triangles congruence, the Class 7 Maths NCERT Solutions Chapter 7 tackles the notion of congruence with the use of practical examples and activities. The SSS, SAS, and ASA congruence theorems, which constitute the foundation for proving triangles congruent, are thoroughly addressed, as is the RHS congruence of right-angles. Chapter 7 Congruence of Triangles of Class 7 Mathematics ensures that all of the congruence ideas are covered in 14 questions, 12 of which are quite straightforward and include a few fill-in-the-blank questions, while the remaining two require the students to draw figures and solve the problems.

7. How can students make full use of NCERT Solutions for Chapter 7 of Class 7 Maths?

The  NCERT Solutions Class 7 Maths Chapter 7  congruence of triangles exercise questions are deliberately constructed to cover the congruence phenomena in all feasible ways with demonstrations of lines, angles, and various sorts of triangles. As a result, students should make full use of these practice questions by extensively practicing them, as this will aid them in tackling other similar types of questions that may appear in exams with comparable patterns.

8. State the important theorems of Chapter 7 of Class 7 Maths.

Two triangles are congruent if they tend to obey the Side-Side-Side(SSS), Side-Angle-Side(SAS), and Angle-Side-Angle(ASA) theorem hypothesis. The two triangles are congruent if the three sides of one are equal to the three sides of the other, according to SSS. Similar precepts apply to SAS and ASA as well.

Congruence of Right-Angled Triangles: They are congruent if the hypotenuse and a leg of one of the right-angled triangles are equal to the hypotenuse and the corresponding leg of the other triangle under a certain correspondence.