Triangles

5 minQuiz at the end

Types of Triangles

By sides:

  • Equilateral: all 3 sides equal, all angles 60Β°
  • Isosceles: 2 sides equal, 2 base angles equal
  • Scalene: no sides equal, no angles equal

By angles:

  • Right-angled: one angle = 90Β°
  • Acute: all angles < 90Β°
  • Obtuse: one angle > 90Β°

Properties

  • Angles in a triangle always sum to 180Β°
  • Exterior angle = sum of the two non-adjacent interior angles
  • The longest side is opposite the largest angle

Triangle Inequality

Any side of a triangle must be less than the sum of the other two sides.

  • 3, 4, 8 β†’ 3 + 4 = 7 < 8 β†’ not a valid triangle

Congruent Triangles

Two triangles are congruent (identical in shape and size) if they satisfy:

  • SSS β€” all three sides equal
  • SAS β€” two sides and the included angle equal
  • ASA β€” two angles and the included side equal
  • RHS β€” right angle, hypotenuse, and one side equal

Similar Triangles

Two triangles are similar if their corresponding angles are equal (same shape, different size). Corresponding sides are in the same ratio.