Triangles are polygons with three sides.Triangle_design.jpg

Angle Properties of Triangles

The interior angles of a triangle always add up to 180°.

( ∠ sum of Δ)

a + b + c = 180°

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

(ext. ∠ of Δ = sum of int.opp ∠s)

w = x + y

The exterior angles of a triangle always add up to 360°.

(sum of ext. ∠s of Δ)


m + n + p = 360°

The smallest angle of a triangle is opposite the smallest side.
The largest angle of a triangle is opposite the largest side.


Types of Triangles

An acute − angled triangle contains no angles greater than 90°


A , B and C are all acute angles.



A right − angled triangle contains an angle of 90°.



A = 90°



An obtuse − angled triangle contains an angle between 90°and 180°. A is an obtuse angle

An isosceles triangle has one axis of symmetry.

An isosceles triangle has two equal sides and two equal angles.

sides: a = b

angles: A =B


An equilateral triangle is one in which all three sides are of equal length and each interior angle is 60°.

An equilateral triangle has three axes of symmetry.


sides: a = b = c

A = 60°
B = 60°
C = 60°

  • Congruent triangles have the same size and shape.
  • Similar triangles have the same shape. The angles of similar triangles are the same, the lengths of the corresponding sides are different
  • If all of the angles and sides are different it is a scalene triangle.