For any triangle, we can draw a line through one point that is parallel to the opposite side. Extending all the sides then creates a diagram with two parallel lines and two transversals, like this:
Let's look at each of these transversals in turn.
Using the first transversal, the angle inside the triangle forms an alternate angle pair:
And using the second transversal, the other angle inside the triangle forms a corresponding angle pair:
This means that the three angles inside the triangle add together to form a straight angle:
In other words: The angle sum of 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.
Consider the triangle below.
Is it a right triangle?
Solve for the value of x in the diagram below.
The angle sum of a triangle is 180\degree.
The exterior angle of a triangle is equal to the sum of the opposite interior angles.
Isosceles triangles have a special property. If two sides are the same, the angles formed with the third side (called the base) are always equal. The reverse is true as well.
What kind of triangle is this?
Isosceles triangles have a special property. If two sides are the same, the angles formed with the third side (called the base) are always equal. The reverse is true as well.