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Tamil Nadu (TNBSE)Class 6 Mathematics★ 5-9 marks in the TN Class 6 Term 2 exam through triangle classification and the triangle inequality

Geometry (Term 2) - Triangles and Lines

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 2 Chapter 4, Geometry. Classifying triangles by their sides and angles, parallel and perpendicular lines, and the triangle inequality (the sum of any two sides is greater than the third), with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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

1Classify triangles by their sides
2Classify triangles by their angles
3Distinguish parallel and perpendicular lines
4Apply the triangle inequality
5Decide whether three lengths form a triangle

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Why this chapter matters

Classifying triangles and knowing when three lengths form a triangle build geometric reasoning. The triangle inequality and classification are directly tested in the TN Class 6 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 lines.

Geometry (Triangles and Lines) — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 2 — Chapter 4. Triangles, parallel and perpendicular lines.

1. About this chapter

This chapter covers the classification of triangles, parallel and perpendicular lines, and the triangle inequality.

2. Classifying triangles

By sides: equilateral (all three sides equal), isosceles (two sides equal), scalene (all sides different).
By angles: acute (all angles less than 90°), right (one 90° angle), obtuse (one angle more than 90°).

3. Parallel and perpendicular lines

Parallel lines are always the same distance apart and never meet (shown by arrows).
Perpendicular lines meet at a right angle (90°), marked with a small square.

4. The triangle inequality

In any triangle, the sum of the lengths of any two sides is greater than the third side.
So 3 cm, 4 cm and 5 cm can form a triangle (3 + 4 > 5), but 2 cm, 3 cm and 6 cm cannot (2 + 3 < 6).

5. Worked examples

Example 1. Classify a triangle with sides 6 cm, 6 cm, 4 cm. Two sides equal → isosceles.

Example 2. Can a triangle have sides 5 cm, 7 cm and 13 cm? 5 + 7 = 12 < 13 → no (fails the triangle inequality).

Example 3. What angle do perpendicular lines make? 90° (a right angle).

6. Exercises (Samacheer Kalvi)

Classify by sides: (a) 5, 5, 5 cm (b) 7, 4, 9 cm (c) 6, 6, 8 cm.
Classify by angles a triangle whose angles are 40°, 60°, 80°.
Can the sides 4 cm, 5 cm and 10 cm form a triangle? Justify.
Draw a pair of (a) parallel lines (b) perpendicular lines.
Name the triangle with all three angles less than 90°.

7. Common mistakes

Mistake: Confusing parallel and perpendicular lines. Fix: Parallel never meet; perpendicular meet at 90°.
Mistake: Ignoring the triangle inequality. Fix: A triangle is possible only if the sum of any two sides > the third.
Mistake: Mixing up classification by sides and by angles. Fix: Sides → equilateral/isosceles/scalene; angles → acute/right/obtuse.

8. Quick revision

Term 2 · Ch 4 · triangles and lines.
By sides: equilateral, isosceles, scalene; by angles: acute, right, obtuse.
Parallel lines never meet; perpendicular lines meet at 90°.
Triangle inequality: the sum of any two sides is greater than the third side.

Key formulas & results

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

By sides

equilateral, isosceles, scalene

Side lengths.

By angles

acute, right, obtuse

Angle measures.

Parallel vs perpendicular

never meet vs meet at 90°

Line relationships.

Triangle inequality

sum of any two sides > third side

Test for a triangle.

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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

✗ Confusing parallel and perpendicular lines

✓ Parallel never meet; perpendicular meet at 90°.

WATCH OUT

✗ Ignoring the triangle inequality

✓ A triangle is possible only if the sum of any two sides is greater than the third.

WATCH OUT

✗ Mixing up classification by sides and by angles

✓ Sides → equilateral/isosceles/scalene; angles → acute/right/obtuse.

NCERT exercises (with solutions)

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

Classify by sides

Equilateral, isosceles, scalene.

Questions

Classify by angles

Acute, right, obtuse.

Questions

Triangle inequality and lines

Test side sets; draw parallel/perpendicular lines.

Questions

Practice problems

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

Q1EASY· By sides

Classify a triangle with sides 6 cm, 6 cm, 4 cm.

▶ Show solution

Isosceles.

Q2MEDIUM· Inequality

Can a triangle have sides 5 cm, 7 cm and 13 cm?

▶ Show solution

No; 5 + 7 = 12 < 13 fails the triangle inequality.

Q3EASY· Lines

What angle do perpendicular lines make?

▶ Show solution

90° (a right angle).

Q4EASY· By angles

Classify a triangle with angles 40°, 60°, 80°.

▶ Show solution

Acute-angled (all angles less than 90°).

Q5EASY· By sides

Classify a triangle with sides 7, 4, 9 cm.

▶ Show solution

Scalene (all sides different).

Q6MEDIUM· Inequality

Can the sides 4 cm, 5 cm and 10 cm form a triangle?

▶ Show solution

No; 4 + 5 = 9 < 10, so it fails the triangle inequality.

5-minute revision

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

•Term 2 Chapter 4 of Samacheer Kalvi Class 6 Maths.
•By sides: equilateral (all equal), isosceles (two equal), scalene (all different).
•By angles: acute (all < 90°), right (one 90°), obtuse (one > 90°).
•Parallel lines never meet; perpendicular lines meet at 90°.
•Triangle inequality: the sum of any two sides is greater than the third.
•Three lengths form a triangle only if they satisfy this inequality.

Tamil Nadu (TNBSE) marks blueprint

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

Typical chapter weightage: 5-9 marks across triangles and lines

Question type	Marks each	Typical count	What it tests
Classification	1	3-4	By sides and by angles
Triangle inequality	2	1-2	Testing side sets
Lines	1	1	Parallel/perpendicular

Prep strategy

Separate side and angle classification
Add the two smaller sides to test a triangle
Remember perpendicular = 90°
Draw neat parallel and perpendicular lines

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 strength to frames and trusses.

Design

Parallel and perpendicular lines shape buildings and grids.

Engineering

The triangle inequality checks if parts can join.

Exam strategy

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

State classification by both sides and angles
Test the two smaller sides for a triangle
Mark right angles with a square
Distinguish parallel and perpendicular clearly

Going beyond the textbook

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

If two sides of a triangle are 6 cm and 9 cm, find the range of the third side.
Draw a triangle that is both scalene and obtuse-angled.

Where else this chapter is tested

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

TN Class 6 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.

Add the two shorter lengths; if their sum is greater than the longest length, the three can form a triangle, otherwise they cannot.

Yes — a triangle can have one right angle and two equal sides at the same time, so it is classified as a right isosceles triangle.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 6 mock tests

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Mathematics flashcards

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