## Triangles

Triangles are polygons with three sides.

### Types of Triangles An acute − angled triangle contains no angles greater than 90°. e.g. A , B and C are all acute angles. A right − angled triangle contains an angle of 90°. e.g. A = 90° An obtuse − angled triangle contains an angle between 90°and 180°. • A scalene triangle contains three sides unequal in length. All angle sizes are different.
• An isosceles triangle is one in which two of the sides and their opposite angles are equal.
• An equilateral triangle is one in which all tree of the sides are equal and each angle is 60°.
• Congruent triangles have the same size and shape.
• Similar triangles have the same shape.

### Symmetry of Triangles

 An isosceles triangle has two equal sides and two equal angles .An isosceles triangle has one axis of symmetry. e.g. 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. e.g. sides: a = b = c angles: A = B = C = 60o ### Properties of Triangles

 The interior or inside angles of a triangle always add up to 180°. They are supplementaryangles. a + b + c = 180° An exterior angle of a triangle is equal to the sum of the two opposite interior angles. w = x + y The exterior angles of a triangle always add up to 360°. 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.