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Class 10th Mathematics Chapter 6 Triangles – Notes

Class 10 Maths Chapter 6 – Basic proportionality theorem, similarity, Pythagoras. NCERT notes.

Topics covered in Triangles

Frequently asked questions

What topics are covered in Class 10th Mathematics Chapter 6 Triangles notes?

This chapter covers: Basic proportionality theorem, Similarity of triangles, AA, SSS, SAS similarity, Pythagoras theorem.

Are Triangles notes free?

Yes, Notebook gives free NCERT CBSE notes for Class 10 Mathematics.

How to prepare Triangles for Class 10 Mathematics exams?

Read the Triangles notes first, revise the key topics (Basic proportionality theorem, Similarity of triangles, AA, SSS, SAS similarity, Pythagoras theorem), then practise the important questions and previous year questions (PYQ) for this chapter.

Where can I find Class 10th Mathematics Chapter 6 Triangles notes for quick revision?

You are on the right page: this notes page for Triangles covers Class 10 Mathematics for the CBSE exam 2026-27. Use the tabs on this chapter for notes, important questions and PYQ.

Is Class 10th Mathematics Chapter 6 Triangles important for the CBSE exam 2026-27?

Triangles is part of the Class 10 Mathematics NCERT CBSE syllabus. Notebook gives notes, important questions and PYQs for it, free.

Also see: Class 10th Mathematics Chapter 6 Triangles Important Questions · Class 10th Mathematics Chapter 6 Triangles PYQ

Triangles

Similar Triangles

Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional. Similar ≠ congruent. Congruent triangles are always similar but not vice versa. The ratio of areas of two similar triangles = square of the ratio of their corresponding sides.

Criteria for Similarity

AA (Angle-Angle): two angles equal → triangles similar. SSS: all three sides proportional → similar. SAS: one angle equal and adjacent sides proportional → similar. These are the main similarity criteria used to solve problems.

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sides in the same ratio. If DE ∥ BC in △ABC, then AD/DB = AE/EC. Converse is also true.

Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse = sum of squares of the other two sides: AC² = AB² + BC². Converse: if AC² = AB² + BC², angle B = 90°. Used extensively in coordinate geometry and real-life problems.

Basic Proportionality Theorem (Thales Theorem)

Statement: If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. Formally: In ΔABC, if DE ∥ BC and D is on AB, E is on AC, then AD/DB = AE/EC. Converse: If a line divides two sides of a triangle in the same ratio, it is parallel to the third side. Proof uses areas of triangles with equal height. This theorem is the foundation for similar triangles and is extremely important for board exams.

Criteria for Similarity of Triangles

Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional. Criteria: (1) AA (Angle-Angle): two pairs of equal angles → triangles are similar; (2) SSS: all three sides proportional → similar; (3) SAS: two sides proportional and included angle equal → similar. In similar triangles ΔABC ~ ΔPQR: AB/PQ = BC/QR = CA/RP and corresponding angles are equal. Ratio of areas of similar triangles = square of ratio of corresponding sides.

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