Triangles are polygons with three sides.

Types of Triangles
Properties of Triangles

Types of TrianglesTriangle_design.jpg

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

e.g. Triangles_04.gifA , Triangles_04.gifB and Triangles_04.gifC are all acute angles.

Triangles_01.gif
 

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

e.g. Triangles_04.gifA = 90°

Triangles_02.gif

An obtuse − angled triangle contains an angle between 90°and 180°. Triangles_03.gif
  • 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: Triangles_04.gifA = Triangles_04.gifB

Triangles_05.gif

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:

Triangles_04.gifA = Triangles_04.gifB = Triangles_04.gifC = 60o

Triangles_07.gif

 

Properties of Triangles

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

They are supplementaryangles.

a + b + c = 180°
Triangles_08.gif
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. w = x + y Triangles_09.gif
The exterior angles of a triangle always add up to 360°. m + n + p = 360°
Triangles_10.gif
  • The smallest angle of a triangle is opposite the smallest side.
  • The largest angle of a triangle is opposite the largest side.