TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27
Chapter 6: Triangles
Detailed Notes • Worked Examples • Competency • Board Practice
📖 Chapter Explanation
Triangles are studied through similarity, proportionality and the relationships created by parallel lines. Similar figures have the same shape while corresponding lengths are proportional.
🧭 Concept Journey
📌 Core Concepts
If two triangles are similar, corresponding sides are proportional. For ΔABC∼ΔDEF, AB/DE=BC/EF=CA/FD. Similarity is about shape and scale, not necessarily equal size.
💡 Worked Example
If two triangles are similar, corresponding sides are proportional. For ΔABC∼ΔDEF, AB/DE=BC/EF=CA/FD. Similarity is about shape and scale, not necessarily equal size.
⚠️ Common Errors
A common mistake is matching sides without matching corresponding angles. Always establish the correct correspondence before writing a proportion.
🧠 Concept-Based MCQs
- If ΔABC∼ΔDEF and AB/DE=2/3, then BC/EF is: A) 1/3 B) 2/3 C) 3/2 D) 2
- The Basic Proportionality Theorem involves a line: A) perpendicular to every side B) parallel to one side of a triangle C) outside the triangle only D) equal to an angle
- Similar triangles have corresponding angles: A) unequal B) supplementary C) equal D) random
- If the scale factor is 3, corresponding lengths are multiplied by: A) 1/3 B) 2 C) 3 D) 9
Answer Key: 1-B, 2-B, 3-C, 4-C.
📊 Case-Based / Competency
A 6 m pole casts a 4 m shadow while a building casts a 20 m shadow at the same time. Explain how similarity can be used to estimate the building’s height.
- Draw or identify the mathematical model.
- Select the relevant theorem/formula.
- Solve with complete working.
- Interpret and verify the answer.
🔎 Extension Case
Surveyors use similar triangles to estimate inaccessible heights. Students identify the corresponding triangles, set up proportions and explain why the same scale factor applies.
🔥 HOTS & Board Challenge
- Explain why the chosen method works.
- Create a similar problem and solve it.
- Find and correct a plausible incorrect solution.
- Apply the concept to a new context.
✍️ Exam Practice
- Define the central concept.
- Solve a direct application problem.
- Solve a multi-step competency problem.
- Interpret a diagram/context.
- Write a 5-mark solution with reasoning.
📄 Practice Worksheet
- 5 concept checks
- 5 standard problems
- 3 applications
- 2 case-based questions
- 2 HOTS questions
- 1 board challenge
🎯 One-Minute Revision
similarity → proportional sides → angle relationships → Basic Proportionality Theorem → similarity criteria → applications
🏆 Mastery Checklist
- ☐ I understand the concept.
- ☐ I can choose the correct method.
- ☐ I can solve step by step.
- ☐ I can handle competency questions.
- ☐ I can verify and interpret my answer.
← Class 10 Mathematics Free Resources | ← Class 10 Main Page
Original explanatory study material aligned to NCERT/CBSE topics; textbook passages are not reproduced verbatim.