Whenever three points do not lie on the same line, we can connect them together with three segments. This three-sided shape is called a triangle. Three angles are formed at the same time (which is how the shape gets its name).
The kinds of angles that are formed lets us classify different types of triangles:
If all the angles are acute, the triangle is an acute triangle.
If one of the angles is a right angle, the triangle is a right-angled triangle.
If one of the angles is obtuse, the triangle is an obtuse triangle.
The lengths of the sides allow us to classify different types of triangles in a completely different way:
If all the sides have different lengths, the triangle is a scalene triangle
If at least two sides have the same length, the triangle is an isosceles triangle
A special kind of isosceles triangle is the equilateral triangle, where all three sides have the same length.
Triangles for each combination of types exist, and this is summarised in the diagram below:
Equilateral triangles are always acute isosceles triangles.
Use the following applet to explore more on the different types of triangles.
A triangle classification can be changed by adjusting the lengths of two sides.
Consider the triangle below.
Which of the following words describes this triangle?
Which of the following words also describes this triangle?
Triangles can be classified by their angles and their sides as shown in the diagram below:
Equilateral triangles are always acute isosceles triangles.
For any triangle, we can draw a line through one point that is parallel to the opposite side.
Using what we learned in the last lesson , let's look at each of these transversals in turn.
In other words: the sum of the angles in a triangle is 180\degree.
Consider the triangle below.
Is it a right-angled triangle?
The sum of the angles in a triangle is 180\degree.
The angles formed outside the triangle by extending the sides are called exterior angles. The size of an exterior angle is always equal to the sum of the internal angles on the opposite side.
Solve for the value of x in the diagram below.
An exterior angle is equal to the sum of the opposite interior angles.