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.
Consider the triangle below.
Which of the following words describes this triangle?
Which of the following words also describes this triangle?
Select all isosceles triangles:
Triangles can be classified by their angles and their sides as shown in the diagram below:
Note: Equilateral triangles are always acute because they always have three 60\degree angles.
If we increase one side while keeping the other two sides the same size the side that is getting longer will also have the opposite angle get bigger. A triangle that has two sides that are the same length means the opposite angles must also be equal.
We can compare the two sets of sides to see what is the defining difference.
We can see that for any side we look at, the other two side lengths when combined are longer.
For the impossible sides, two of the sides we can choose the other two sides combined are longer. However, looking at the longest side, the two shorter sides combined are still smaller than the longest side. This is the condition which determines whether a triangle is possible or not. For a triangle the combined length of each pair of sides is longer than the remaining side.
Is it possible to form a triangle with side lengths 13,\,7, and 6?
Which side is the shortest side of the triangle?
For a triangle to be possible with all three sides, the combined length of each pair of sides is longer than the remaining side.