CBSE Class 7 Mathematics NCERT Solutions: Chapter 7 Congruence of Triangles

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NCERT Solutions PDF Class 7 PDF

CBSE Class 7 Mathematics Chapter 7, Congruence of Triangles, introduces the core idea of congruence in geometry, with a special focus on triangles. This chapter delves into identifying congruent shapes, line segments, and angles, providing clear explanations and detailed solutions. Students will explore the conditions required for triangles to be congruent and learn to pinpoint corresponding parts in congruent triangles. These solutions aim to establish a solid understanding of geometric principles, enabling students to grasp the characteristics of congruent figures and use them to solve various problems. A firm grasp of these concepts is essential for future, more complex geometry topics and serves as a valuable tool for exam preparation.

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Quick info

BoardCBSE
ClassClass 7
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 7: Congruence of Triangles

Chapter summary

Chapter 7 of the CBSE Class 7 Mathematics NCERT Solutions focuses on the concept of congruence. It covers the definition of congruent line segments, angles, and shapes, providing real-time examples. The chapter emphasizes understanding the correspondence between vertices, sides, and angles of congruent triangles and how to write congruence statements. The exercises guide students in identifying corresponding congruent parts based on given congruence relations.

Learning outcomes

  • Understand the definition of congruent line segments and angles.
  • Identify real-world examples of congruent shapes.
  • Write congruence statements for triangles.
  • Identify corresponding congruent parts (angles and sides) of congruent triangles.
  • Understand the notation used for congruence.

Topics covered

Paper topics

  • Congruence of Line Segments
  • Congruence of Angles
  • Congruence of Triangles
  • Corresponding Parts of Congruent Triangles
  • Notation for Congruence
  • Real-time Examples of Congruent Shapes

Important topics

  • Understanding Congruence
  • Identifying Corresponding Parts
  • Writing Congruence Statements
  • Congruence of Angles and Line Segments

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Questions and Solutions

Question 1

Complete the following statements:

(a) Two line segments are congruent if ______.

(b) Among two congruent angles, one has a measure of 70°, the measure of the other angle is ______.

(c) When we write \angle A = \angle B, we actually mean _____.

Solution:

The concept of congruence means that two figures are identical in both shape and size. We can apply this to line segments and angles:

(a) Two line segments are considered congruent if they have the exact same length. This means one segment can be placed perfectly on top of the other.

(b) If two angles are congruent, they must have the same measure. Therefore, if one angle measures 70°, the other congruent angle must also measure 70°.

(c) The statement \angle A = \angle B is a concise way of saying that the measures of angle A and angle B are equal. Mathematically, this is written as m\angle A = m\angle B.

Question 2

Give any two real-time examples for congruent shapes.
Solution:

Congruent shapes are objects that are identical in form and size. Here are two real-time examples:

  1. Two identical footballs: All standard footballs are manufactured to be the same size and shape, making them congruent to each other.
  2. Two teacher's tables in a classroom: If a school purchases identical tables for its classrooms, each table will be congruent to the others.

Question 3

If \triangle ABC \cong \triangle FED under the correspondence ABC \leftrightarrow FED, write all the corresponding congruent parts of the triangles.
Solution:

Given the congruence statement \triangle ABC \cong \triangle FED, the order of the vertices is crucial for identifying the corresponding parts. The correspondence is ABC \leftrightarrow FED.

The corresponding congruent parts are:

  1. Corresponding Angles:
    • \angle A corresponds to \angle F
    • \angle B corresponds to \angle E
    • \angle C corresponds to \angle D
  2. Corresponding Sides:
    • Side \overline{AB} corresponds to side \overline{FE}
    • Side BC corresponds to side \overline{ED}
    • Side \overline{AC} corresponds to side \overline{FD}

Question 4

If \Delta DEF \cong \Delta BCA, write the part(s) of \Delta BCA that correspond to:

(i) \angle E

(ii) \overline{\mathrm{EF}}

(iii) \angle F

(iv) \overline{\mathrm{DF}}
Solution:

We are given the congruence statement \Delta DEF \cong \Delta BCA. This statement establishes a specific correspondence between the vertices of the two triangles: D \leftrightarrow B, E \leftrightarrow C, and F \leftrightarrow A.

Using this correspondence, we can identify the parts of \Delta BCA that correspond to the given parts of \Delta DEF:

(i) The angle \angle E in \Delta DEF corresponds to the angle \angle C in \Delta BCA.

(ii) The side \overline{\mathrm{EF}} in \Delta DEF corresponds to the side \overline{\mathrm{CA}} in \Delta BCA.

(iii) The angle \angle F in \Delta DEF corresponds to the angle \angle A in \Delta BCA.

(iv) The side \overline{\mathrm{DF}} in \Delta DEF corresponds to the side \overline{\mathrm{BA}} in \Delta BCA.

Common mistakes

  • Confusing congruence with similarity.
  • Incorrectly identifying corresponding vertices, sides, or angles.
  • Not writing the congruence statement with the correct order of vertices.
  • Misinterpreting the notation for angles and line segments.

Revision tips

  • Review the definitions of congruent line segments, angles, and shapes thoroughly.
  • Practice identifying corresponding parts in different congruence scenarios.
  • Draw diagrams to visualize congruent triangles and their corresponding parts.
  • Use the provided real-time examples to reinforce the concept of congruence.

Practice MCQs

Q1. Two line segments are congruent if they have:

Q2. If two angles are congruent and one measures 70°, what is the measure of the other angle?

Q3. What does the statement \angle A = \angle B mean in terms of angle measures?

Q4. If \triangle ABC \cong \triangle FED, which side corresponds to side AC?

Q5. Which angle corresponds to \angle E in \triangle DEF \cong \triangle BCA?

Frequently asked questions

What is congruence in geometry?

Congruence means that two geometric figures have the same shape and the same size. They are identical and can be superimposed perfectly on each other.

How do we know if two line segments are congruent?

Two line segments are congruent if and only if they have the same length.

What does it mean for two angles to be congruent?

Two angles are congruent if they have the same measure. For example, if \angle A = 70°, then any angle congruent to \angle A will also measure 70°.

How are corresponding parts of congruent triangles identified?

The order of vertices in the congruence statement (e.g., \triangle ABC \cong \triangle FED) indicates the correspondence. \angle A corresponds to \angle F, \angle B to \angle E, \angle C to \angle D, side AB to side FE, side BC to side ED, and side AC to side FD.

Can you give a real-time example of congruent shapes?

Yes, two identical coins, two identical playing cards, or two identical footballs are examples of congruent shapes.

What is the significance of writing \angle A = \angle B?

Writing \angle A = \angle B is a shorthand notation that means the measure of angle A is equal to the measure of angle B (m\angle A = m\angle B).

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