Chapter Hub
Triangles
This chapter focuses on how triangles compare in shape, how parallel lines divide sides, and how similarity helps in proving many useful relations. For Class 10 CBSE, the main ideas are similarity criteria, the Basic Proportionality Theorem, area ratio, and right-triangle relations. Students should learn the exact conditions first, then practice applying them in numerical problems and proof-based questions. A good revision of this chapter means knowing when to use angle comparison, side ratios, square checks, and scale factor ideas correctly.
Difficulty
Medium
Study time
96-120 min
Plan by time
Pick the window that matches what you have right now.
If you have 15 min
Last-pass revision
Skim the Quick Revision table — definitions, formulas, and the traps board examiners reuse.
Open Quick RevisionIf you have 45 min
Targeted practice
Read the high-priority concepts, then take the chapter MCQ quiz to find weak spots.
Start MCQ QuizIf you have 96 min
First full pass
Walk every concept in chapter order, then revise and quiz. Best for the first time you study this chapter.
Open Key ConceptsChapter Learning Map
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Key Concepts
Concepts grouped the way the chapter is taught — open the bucket that matches what you want to revise.
Core Concepts
high priorityOpen the chapter concepts in a clean revision order.
Similarity of triangles
Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio.
AAA similarity criterion
If three angles of one triangle are respectively equal to three angles of another triangle, the triangles are similar.
SAS similarity criterion
Two triangles are similar if one included angle is equal and the two sides around that angle are proportional.
SSS similarity criterion
Two triangles are similar if all three corresponding sides are proportional.
Basic proportionality theorem
A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.
Converse of basic proportionality theorem
If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side.
Area ratio of similar triangles
For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides.
Pythagoras theorem
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Converse of Pythagoras theorem
If the square of the longest side of a triangle equals the sum of the squares of the other two sides, the triangle is right-angled.
Altitude to hypotenuse relations
In a right triangle, the altitude from the right angle to the hypotenuse creates two smaller triangles that are similar to the original triangle and to each other.
Using similarity to prove relations
Once two triangles are proved similar, you can use corresponding side ratios and equal angles to prove lengths, proportions, and parallel-line results.
Scale factor in similar triangles
The scale factor is the number by which one similar triangle is enlarged or reduced to get the other.
Exam Intelligence
Use this section to decide what deserves the most revision time.
High Probability Topics
- Similarity of triangles
- AAA similarity criterion
- SAS similarity criterion
- SSS similarity criterion
- Basic proportionality theorem
- Converse of basic proportionality theorem
- Area ratio of similar triangles
- Pythagoras theorem
Common Traps
- Mixing up corresponding vertices and writing ratios in the wrong order.
- Using side equality where only proportionality is needed.
- Forgetting to square the side ratio for area ratio questions.
- Using Pythagoras theorem in a triangle that is not right-angled.
- Checking the wrong side in the converse of Pythagoras theorem.
- Adding hypotenuse segments instead of using the product relation in altitude problems.
Likely Question Types
- MCQ: concept checks, applications, and common mistakes
- Very short answer: definitions, formulas, or conditions
- Short answer: worked method, example, or reason-based explanation
- Case-based: chapter scenario with concept-linked subparts
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
- Similarity means same shape, not necessarily same size.
- AAA, SAS, and SSS are the three standard similarity criteria.
- BPT and its converse connect parallel lines with proportional side division.
- Area ratio follows the square of the side ratio.
- Pythagoras theorem and its converse apply only with right-triangle square checks.
- Altitude to hypotenuse problems often use the relation h² = pq.
- Similarity of triangles: Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio.
- AAA similarity criterion: If three angles of one triangle are respectively equal to three angles of another triangle, the triangles are similar.
Practice
Use short concept checks first, then move into the full chapter test.
Free Chapter MCQ Quiz
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