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Triangles Class 10 Maths — Revision Notes

This chapter focuses on properties of triangles including congruence, similarity, and the Pythagoras theorem. Students learn criteria for triangle congruen

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TL;DR: This chapter focuses on properties of triangles including congruence, similarity, and the Pythagoras theorem. Students learn criteria for triangle con…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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This chapter focuses on properties of triangles including congruence, similarity, and the Pythagoras theorem. Students learn criteria for triangle congruen

Triangle Congruence

  • Two triangles are congruent if they have same shape and size
  • SSS criterion: all sides equal
  • SAS criterion: two sides and included angle equal
  • ASA criterion: two angles and included side equal
  • AAS criterion: two angles and non-included side equal

Triangle Similarity

  • Two triangles are similar if corresponding angles are equal and sides are proportional
  • AA criterion: two angles equal (implies third equal)
  • SSS criterion: all sides proportional
  • SAS criterion: two sides proportional and included angle equal
  • Similar triangles have same shape but different sizes

Pythagoras Theorem

  • In right triangle: a^2 + b^2 = c^2 where c is hypotenuse
  • Converse: if a^2 + b^2 = c^2, then triangle is right-angled
  • Used to find missing side in right triangle
  • Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17)

Basic Proportionality Theorem

  • If line parallel to one side of triangle intersects other two sides, it divides them proportionally
  • If AB/AD = AC/AE, then DE is parallel to BC
  • Angle bisector theorem: angle bisector divides opposite side in ratio of adjacent sides
  • These theorems used in geometric proofs and constructions

Key Terms

  • Congruent Triangles: Triangles having same shape and size with all corresponding parts equal
  • Similar Triangles: Triangles having same shape with corresponding angles equal and sides proportional
  • Hypotenuse: Longest side of right triangle opposite the right angle

Frequently Asked Questions

What is the difference between congruence and similarity?

Congruent triangles have same shape and size (all sides and angles equal). Similar triangles have same shape but different sizes (angles equal, sides proportional).

How do you prove two triangles are congruent?

Use one of the criteria: SSS (all sides equal), SAS (two sides and included angle), ASA (two angles and included side), or AAS (two angles and non-included side).

More Class 10 Maths Revision Notes

  • Real Numbers
  • Polynomials
  • Pair of Linear Equations in Two Variables
  • Quadratic Equations
  • Arithmetic Progressions
  • Coordinate Geometry

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More free resources for this chapter

  • NCERT Solutions →
  • Important Questions →
  • MCQ Practice →
  • Previous Year Questions →
  • State Board Solutions →
  • Formula Sheet →

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