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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 2 exam through angle and congruence questions

Geometry (Term 2) - Triangles and Congruence

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 2 Chapter 4, Geometry (Triangles). Classifying triangles by sides and angles, the angle-sum property and the exterior-angle property, the congruence criteria (SSS, SAS, ASA, RHS) and an introduction to similarity, with worked examples, exercises and quick revision.

⏱ 15 min readMedium difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Classify triangles by sides and angles
2Apply the angle-sum property
3Apply the exterior-angle property
4State and use the congruence criteria (SSS, SAS, ASA, RHS)
5Distinguish congruence from similarity

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Why this chapter matters

Triangles and their congruence are central to geometry and proof. The angle-sum and exterior-angle properties and the congruence criteria are directly tested in the TN Class 7 Term 2 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Term 1 — Geometry (Lines and Angles)

Angles and angle pairs.

Geometry (Triangles and Congruence) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 2 — Chapter 4. Triangles, their properties and congruence.

1. About this chapter

This chapter covers the classification of triangles, the angle-sum and exterior-angle properties, the criteria for congruence of triangles, and an introduction to similarity.

2. Classifying triangles

By sides: equilateral (all sides equal), isosceles (two sides equal), scalene (all sides different).
By angles: acute (all angles < 90°), right (one 90° angle), obtuse (one angle > 90°).

3. Properties of a triangle

Angle-sum property: the three angles of a triangle add up to 180°.
Exterior-angle property: an exterior angle equals the sum of the two opposite interior angles.

4. Congruence of triangles

Two triangles are congruent (exactly the same shape and size) if they satisfy any one criterion:

Criterion	Meaning
SSS	all three sides equal
SAS	two sides and the included angle equal
ASA	two angles and the included side equal
RHS	in right triangles: hypotenuse and one side equal

Similar triangles have the same shape (equal angles) but not necessarily the same size; their sides are in proportion.

5. Worked examples

Example 1. Two angles of a triangle are 50° and 60°. Find the third. 180° − (50° + 60°) = 70°.

Example 2. An exterior angle of a triangle is 120°; one opposite interior angle is 70°. Find the other. 120° − 70° = 50°.

Example 3. Which criterion proves two triangles congruent if all three sides are equal? SSS.

6. Exercises (Samacheer Kalvi)

Classify by sides and angles: a triangle with sides 5, 5, 5 cm.
Two angles of a triangle are 45° and 95°. Find the third angle.
The exterior angle of a triangle is 110°; one interior opposite angle is 65°. Find the other.
State the congruence criterion: two triangles have two angles and the included side equal.
Are an equilateral triangle of side 3 cm and one of side 6 cm congruent or similar?

7. Common mistakes

Mistake: Thinking the angle sum can exceed 180°. Fix: The three angles always add to exactly 180°.
Mistake: Using "AAA" as a congruence criterion. Fix: Equal angles only prove similarity, not congruence (no AAA congruence).
Mistake: Confusing the included angle in SAS. Fix: SAS needs the angle between the two equal sides.

8. Quick revision

Term 2 · Ch 4 · triangles.
By sides: equilateral / isosceles / scalene; by angles: acute / right / obtuse.
Angle sum = 180°; exterior angle = sum of two opposite interior angles.
Congruence: SSS, SAS, ASA, RHS. Similar = same shape, sides in proportion (not necessarily same size).

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Angle-sum

angle1 + angle2 + angle3 = 180°

Always exact.

Exterior angle

exterior = sum of two opposite interior angles

Triangle property.

Congruence criteria

SSS, SAS, ASA, RHS

No AAA congruence.

Similarity

equal angles; sides in proportion

Same shape, maybe different size.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Thinking the angle sum can exceed 180°

✓ The three angles always add to exactly 180°.

WATCH OUT

✗ Using 'AAA' as a congruence criterion

✓ Equal angles only prove similarity, not congruence (no AAA congruence).

WATCH OUT

✗ Confusing the included angle in SAS

✓ SAS needs the angle between the two equal sides.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Classification

Classify triangles by sides and angles.

Questions

Angle properties

Angle-sum and exterior-angle sums.

Questions

Congruence

Apply the congruence criteria.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Angle-sum

Two angles of a triangle are 50° and 60°. Find the third.

▶ Show solution

70°.

Q2EASY· Classify

Classify a triangle with sides 5, 5, 5 cm.

▶ Show solution

Equilateral (and acute-angled).

Q3MEDIUM· Exterior angle

An exterior angle is 110°; one interior opposite angle is 65°. Find the other.

▶ Show solution

110° − 65° = 45°.

Q4EASY· Congruence

Name the criterion when two angles and the included side are equal.

▶ Show solution

ASA.

Q5MEDIUM· Concept

Are equilateral triangles of side 3 cm and 6 cm congruent or similar?

▶ Show solution

Similar (same shape, sides in proportion) but not congruent (different size).

Q6MEDIUM· Angle-sum

Two angles of a triangle are 45° and 95°. Find the third and classify by angle.

▶ Show solution

Third = 40°; the triangle is obtuse-angled (has a 95° angle).

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 2 Chapter 4 of Samacheer Kalvi Class 7 Maths.
•By sides: equilateral, isosceles, scalene; by angles: acute, right, obtuse.
•Angle-sum property: the three angles add to 180°.
•Exterior-angle property: an exterior angle equals the sum of the two opposite interior angles.
•Congruence criteria: SSS, SAS, ASA, RHS (no AAA).
•Similar triangles have equal angles and sides in proportion (same shape, maybe different size).

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across angle and congruence work

Question type	Marks each	Typical count	What it tests
Objective	1	3-4	Classification and criteria
Angle property	2	1-2	Angle-sum / exterior angle
Congruence reasoning	2	1	Choosing the right criterion

Prep strategy

Use the 180° angle sum to find missing angles
Remember the exterior-angle shortcut
Memorise SSS, SAS, ASA, RHS
Distinguish congruence from similarity

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Construction

Triangles give rigidity to bridges and trusses.

Design

Congruent shapes tile patterns and logos.

Measurement

Similar triangles help find unknown heights and distances.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Apply the 180° rule for missing angles
Use the exterior-angle property as a shortcut
Quote the exact congruence criterion
Separate congruence from similarity in answers

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Prove the exterior-angle property using the angle-sum property.
Two triangles share two equal angles and one equal side — when are they congruent?

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 2 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Two triangles can have all three angles equal but be different sizes (like a small and a large equilateral triangle), so equal angles guarantee only the same shape — that is similarity, not congruence.

Congruent triangles are identical in both shape and size; similar triangles have the same shape (equal angles) and proportional sides but may differ in size.

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