Chapter 6 · Class X Mathematics · NCERT Exercises

Triangles — Exercises

Similarity · Pythagoras · Criteria — Every Triangle Theorem Applied

📂 6 Exercises 📝 65 Questions 🎓 High

▶ Start Exercises 📖 Revise Notes

Exercise Index

Similar figures; Basic Proportionality Theorem (Thales)

BPT; converse; parallel lines in triangles

Similarity criteria: AA, SSS, SAS; corresponding sides and angles

16 Q Moderate-Hard

Areas of similar triangles; ratio of areas = square of ratio of sides

Pythagoras Theorem; converse; applications

17 Q Moderate-Hard

Combined proofs; median-altitude; real geometry problems

6 exercise files · 65 total questions

Chapter at a Glance

CBSE BoardsNTSEOlympiad

12 Concepts

10 Formulas

High Difficulty

10–12% Weightage

Before You Begin

Prerequisites

✓Congruence of triangles (Class IX)
✓Properties of quadrilaterals
✓Basic proportionality

Have Ready

🔧Geometry compass and ruler
🔧Protractor
🔧NCERT theorems list

Exercise Topic Map

Exercise 6.1 Identify similar shapes; state BPT: DE∥BC ⟹ AD/DB = AE/EC

Exercise 6.2 Apply BPT and converse in diagrams; prove lines parallel or find unknown ratios

Exercise 6.3 State similarity criterion (AA/SSS/SAS); write vertices in order; state all corresponding elements

Exercise 6.4 Area(△1)/Area(△2) = (corresponding side ratio)²; combine with similarity

Exercise 6.5 In right △: hyp² = base²+perp²; converse: if c²=a²+b² → right angle at C

Miscellaneous Multi-step proofs using BPT + similarity + Pythagoras together

Key Formulae — Recall Before Solving

\(\dfrac{AD}{DB} = \dfrac{AE}{EC} \quad \text{(BPT: DE} \parallel \text{BC)}\)

\(\dfrac{\text{Area}(\triangle_1)}{\text{Area}(\triangle_2)} = \dfrac{AB^2}{DE^2} = \dfrac{BC^2}{EF^2}\)

\(AC^2 = AB^2 + BC^2 \quad \text{(Pythagoras)}\)

\(\triangle ABC \sim \triangle DEF \Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{CA}{FD}\)

NCERT Solving Method

Step 1 — BPT: confirm DE∥BC first using given angle or side info. Step 2 — Similarity: identify known angles/sides; choose appropriate criterion (AA preferred when angles available). Step 3 — Always write similar triangles with vertices in CORRECT corresponding order. Step 4 — Pythagoras converse: compute all three squares; check if largest = sum of other two.

Continue Your Preparation

📖NotesTheory & concepts 🧠MCQsTopic-wise practice ⚖️True–FalseConcept check ➡️Next ChapterCoordinate Geometry

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