Chapter 5 of 7

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Tamil Nadu (TNBSE)Class 8 Mathematics★ 6-10 marks in the TN Class 8 annual exam through MCQs, congruence, Pythagoras and construction problems

Geometry

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 5, Geometry. Congruence of triangles (SSS, SAS, ASA, RHS), similarity versus congruency, the Pythagoras property, and the construction of quadrilaterals. Notes with theorems, worked examples, common mistakes, book-back practice and quick revision.

⏱ 20 min readMedium difficulty✓ Free · NCERT-aligned

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

1Apply triangle congruence criteria
2Distinguish similar and congruent figures
3Use the Pythagoras property
4Construct quadrilaterals from given measurements
5Identify the RHS criterion for right triangles

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Why this chapter matters

Geometry develops reasoning through congruence, similarity and the Pythagoras property, and practical skill through constructions. These are reliable scoring areas in the TN Class 8 exam and build toward Class 9 geometry.

Before you start — revise these

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

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Class 7 — Triangles

Triangle properties and angles.

Geometry — Class 8 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 8 Mathematics, Chapter 5. Congruence, similarity, Pythagoras and constructions.

1. About this chapter

This chapter covers congruence of triangles, similarity vs congruency, the Pythagoras property, and the construction of quadrilaterals.

2. Congruence of triangles

Two triangles are congruent if they have exactly the same shape and size.
Criteria: SSS, SAS, ASA, AAS, RHS (RHS for right triangles).
Congruent triangles have equal corresponding sides and angles.

3. Similarity and Pythagoras

Similar figures have the same shape but possibly different size — corresponding angles equal, sides proportional.
Congruent figures are a special case of similar figures (ratio 1 : 1).
Pythagoras property: in a right triangle, hypotenuse² = base² + height².

4. Construction of quadrilaterals

A quadrilateral can be constructed when 5 suitable measurements are given (e.g., four sides and a diagonal; or sides and angles).
Special quadrilaterals — trapezium, parallelogram, rectangle, rhombus — are constructed from their defining measurements.

5. Worked examples

Example 1. A right triangle has base 6 cm and height 8 cm. Find the hypotenuse. h² = 6² + 8² = 100 → h = 10 cm.

Example 2. Two triangles have all three pairs of sides equal. Are they congruent? Yes — by the SSS criterion.

Example 3. How many measurements are needed to construct a unique quadrilateral? Five suitable measurements.

6. Common mistakes

Mistake: Using SSA as a congruence rule. Fix: Valid rules are SSS, SAS, ASA, AAS, RHS (not SSA).
Mistake: Treating similar figures as congruent. Fix: Similar = same shape (proportional sides); congruent = same shape and size.
Mistake: Using Pythagoras in a non-right triangle. Fix: It applies only to right-angled triangles.

7. Practice (book-back style)

State the congruence criteria for triangles.
A right triangle has legs 5 cm and 12 cm. Find the hypotenuse.
Differentiate similar and congruent figures.
How many measurements are needed to construct a quadrilateral?
Which criterion applies only to right triangles?

8. Answer key

SSS, SAS, ASA, AAS and RHS.
h² = 5² + 12² = 169 → h = 13 cm.
Similar: same shape, proportional sides; congruent: same shape and size (ratio 1:1).
Five measurements.
RHS.

9. Quick revision

Chapter 5 · congruence, similarity, Pythagoras, constructions.
Congruence: SSS, SAS, ASA, AAS, RHS (not SSA).
Similar: proportional sides; congruent: identical (special similar).
Pythagoras: hypotenuse² = base² + height².
A unique quadrilateral needs five suitable measurements.

Key formulas & results

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

Congruence criteria

SSS, SAS, ASA, AAS, RHS

Not SSA.

Pythagoras property

hypotenuse² = base² + height²

Right triangles only.

Similar vs congruent

proportional sides vs identical (ratio 1:1)

Congruent is special similar.

Quadrilateral construction

five suitable measurements

Determines a unique quadrilateral.

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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

✗ Using SSA as a congruence rule

✓ Valid rules are SSS, SAS, ASA, AAS, RHS (not SSA).

WATCH OUT

✗ Treating similar figures as congruent

✓ Similar = same shape (proportional sides); congruent = same shape and size.

WATCH OUT

✗ Using Pythagoras in a non-right triangle

✓ It applies only to right-angled triangles.

NCERT exercises (with solutions)

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

Multiple choice questions

MCQs on congruence, similarity and Pythagoras.

Questions

Congruence / Pythagoras

Apply criteria and the Pythagoras property.

Questions

Constructions

Construct quadrilaterals from measurements.

Questions

Practice problems

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

Q1EASY· Recall

State the congruence criteria for triangles.

▶ Show solution

SSS, SAS, ASA, AAS and RHS.

Q2EASY· Numerical

A right triangle has legs 5 cm and 12 cm. Find the hypotenuse.

▶ Show solution

h² = 5² + 12² = 169 → h = 13 cm.

Q3MEDIUM· Concept

Differentiate similar and congruent figures.

▶ Show solution

Similar figures have the same shape with proportional sides; congruent figures have the same shape and size (ratio 1:1).

Q4EASY· Concept

How many measurements are needed to construct a quadrilateral?

▶ Show solution

Five suitable measurements.

Q5EASY· Concept

Which congruence criterion applies only to right triangles?

▶ Show solution

RHS.

Q6EASY· Numerical

A right triangle has base 6 cm and height 8 cm. Find the hypotenuse.

▶ Show solution

h² = 6² + 8² = 100 → h = 10 cm.

5-minute revision

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

•Chapter 5 of Samacheer Kalvi Class 8 Mathematics.
•Congruence: SSS, SAS, ASA, AAS, RHS (not SSA).
•Similar: proportional sides; congruent: identical (special similar).
•Pythagoras: hypotenuse² = base² + height².
•A unique quadrilateral needs five measurements.
•RHS applies to right triangles.

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 MCQ, congruence, Pythagoras and construction problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Criteria and properties
Congruence / Pythagoras	2-3	1-2	Apply criteria and Pythagoras
Construction	3-5	1	Construct quadrilaterals

Prep strategy

Memorise the congruence criteria
Practise Pythagoras numericals
Separate similarity and congruency
Practise quadrilateral constructions

Where this shows up in the real world

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

Design

Congruence and constructions create accurate figures.

Construction

The Pythagoras property checks right angles on site.

Maps and models

Similarity underlies scale drawings.

Exam strategy

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

Name the correct congruence criterion
Apply Pythagoras only to right triangles
Keep construction arcs visible
Distinguish similar from congruent

Going beyond the textbook

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

Prove two triangles congruent using ASA.
Verify the Pythagoras property for a 3-4-5 triangle and its multiples.

Where else this chapter is tested

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

TN Class 8 Annual ExamHigh

Foundation / NMMS MathematicsMedium

School unit testsHigh

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Questions students ask

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

Congruent figures are similar figures whose ratio of corresponding sides is 1:1 — same shape and the same size.

A quadrilateral has more freedom than a triangle, so five independent measurements (such as four sides and a diagonal) are needed to fix it uniquely.

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