Triangles is a a plane figure bounded by three line segments. The sum of the three interior angles of a triangle is 180º.

Types of Triangles

  1. Scalene Triangle: All the sides are of different lengths.
  2. Isosceles Triangle: A triangle having two sides equal.
  3. Equilateral Triangle: A triangle having all sides equal.
  4. Right-angled Triangle: A triangle in which one of the angles is right angle.
  5. Obtuse angled triangle: A triangle in which one of the angles is obtuse angle.
  6. Acute angled triangle: A triangle in which all the three angles are acute.

The angle formed by a produced side of the triangle and another side of the triangle is called an exterior angle of the triangle. An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Congruent Triangles

Two figures, which have the same shape and same size are called congruent figures. Two line segments are congruent when they are of equal length. Two squares are congruent if their sides are equal.

Two triangles are congruent, if all the sides and all the angles of one are equal to the corresponding sides and angles of other.

Criterion of congruence: SAS, ASA or AAS, SSS, RHS

Similar Triangles

Objects which have the same shape but different sizes are called similar objects. Any two polygons, with corresponding angles equal and corresponding sides proportional are similar.

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.

Criterion for Similarity: AAA, SSS, SAS