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Triangles Class 9 Maths — Revision Notes

This chapter covers triangle properties, congruence criteria, and angle bisectors. Students learn to prove triangle congruence and understand angle-side re

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TL;DR: This chapter covers triangle properties, congruence criteria, and angle bisectors. Students learn to prove triangle congruence and understand angle-si…

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

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This chapter covers triangle properties, congruence criteria, and angle bisectors. Students learn to prove triangle congruence and understand angle-side re

Triangle Classification

  • Equilateral triangle: all sides equal, all angles 60°
  • Isosceles triangle: two sides equal, base angles equal
  • Scalene triangle: all sides different, all angles different
  • Acute: all angles < 90°, Right: one angle = 90°, Obtuse: one angle > 90°

Triangle Congruence

  • SSS criterion: all three sides equal
  • SAS criterion: two sides and included angle equal
  • ASA criterion: two angles and included side equal
  • RHS criterion: right angle, hypotenuse, side equal (right triangles)

Isosceles Triangle Properties

  • Angles opposite equal sides are equal
  • If two angles are equal, opposite sides are equal
  • Median from vertex angle bisects base at right angles
  • All medians, altitudes, angle bisectors from vertex angle coincide

Triangle Angle-Side Relation

  • Angle opposite longer side is larger
  • Side opposite larger angle is longer
  • Triangle inequality: sum of any two sides > third side
  • Pythagoras theorem: in right triangle, a^2 + b^2 = c^2

Key Terms

  • Congruent Triangles: Triangles with same shape and size, all corresponding parts equal
  • Isosceles Triangle: Triangle with two equal sides
  • Median: Line from vertex to midpoint of opposite side

Frequently Asked Questions

How do you prove two triangles are congruent?

Use one of the criteria: SSS (all sides), SAS (two sides and included angle), ASA (two angles and included side), or RHS (right angle, hypotenuse, side).

Why are base angles of isosceles triangle equal?

In isosceles triangle, two sides are equal. The angles opposite these equal sides are equal. These are the base angles.

More Class 9 Maths Revision Notes

  • Number Systems
  • Polynomials
  • Linear Equations in Two Variables
  • Lines and Angles

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