Board Buddy

Page 1: Introduction

Triangles chapter builds on Class 9 congruence and introduces similarity.

Key topics: similarity criteria, BPT (Thales theorem), Pythagoras & converse, area ratios, proofs.

High weightage in boards — many 3-6 mark questions.

Page 2: Similar Triangles

Two triangles similar if corresponding angles equal and corresponding sides proportional.

Symbol ~

Corresponding vertices matched.

Page 3: Criteria for Similarity - AAA

If all three angles of one triangle equal to three angles of another → similar (AAA or AA).

Strongest criterion — two angles sufficient.

Page 4: Criteria - SSS

If all three sides of one triangle proportional to three sides of another → similar.

Page 5: Criteria - SAS

If two sides proportional and included angle equal → similar.

Included angle important.

Page 6: Basic Proportionality Theorem (Thales)

If a line parallel to one side of triangle intersects other two sides, then it divides those sides proportionally.

DE ∥ BC → AD/DB = AE/EC

Page 7: Converse of BPT

If a line divides two sides proportionally → parallel to third side.

Page 8: Area of Similar Triangles

Ratio of areas = (ratio of corresponding sides)²

Very important for numericals.

Page 9: Pythagoras Theorem

In right-angled triangle, hypotenuse² = sum of other two sides²

Proof using similar triangles.

Page 10: Converse of Pythagoras

If square of one side = sum of squares of other two → right-angled at opposite vertex.

Page 11: Key Theorems Summary

AAA, SSS, SAS similarity
BPT and converse
Area ratio = side ratio²
Pythagoras and converse

Page 12: Practice Questions - Easy (1-10)

State BPT.
Similarity symbol.
Pythagoras in right triangle.
Area ratio if sides 2:3.
Which criterion for similarity?
Converse of Pythagoras.
SAS similarity condition.
Parallel line divides proportionally.
Ratio of areas if sides ratio k.
AAA similarity.

Page 13: Practice Questions - Medium (11-20)

Prove BPT using similar triangles.
Find length using BPT numerical.
Area of two similar triangles ratio 4:9, sides?
Verify Pythagoras in given triangle.
Prove converse Pythagoras.
Find unknown side using similarity.
Shadow problem using similarity.
Prove area ratio theorem.
Parallel line segment length.
Check similarity by SSS.

Page 14: Practice Questions - Hard (21-30)

Full proof of BPT.
Advanced shadow height problem.
Triangle divided by parallel lines.
Prove Pythagoras using similarity.
Multiple similar triangles problem.
Area and side combined.
Board level proof question.
Find ratios using converse BPT.
Complex diagram similarity.
Pythagoras application numerical.

Page 15: Important Proofs Recap

BPT, area ratio, Pythagoras.

Page 16: Common Mistakes

Wrong corresponding sides in similarity
Forgetting square in area ratio
Missing included angle in SAS
Wrong proportionality in BPT
Confusing Pythagoras and converse

Page 17: Previous Year Questions

BPT proof, similarity numerical, area ratio, Pythagoras verification.

Page 18: Exam Tips

Draw neat labelled diagrams
State theorem clearly
Show corresponding angles/sides
Write ratio properly
Practice proofs word by word

Page 19: Quick Revision Sheet

All theorems, criteria, formulas.

Page 20: Final Motivation

Chapter 6 complete! Triangles is heavy but scoring.

Master BPT and similarity proofs.

Class 10 Maths unstoppable 🦖

Page 21: Extra Proofs

BPT, area, Pythagoras detailed.

Page 22: Similarity Criteria Table

AAA, SSS, SAS comparison.

Page 23: Area Ratio Examples

Numerical practice.

Page 24: Pythagoras Applications

Right triangle problems.

Page 25: Board Pattern Questions

Common types.

Class 10 Mathematics