Triangles
Last updated: 15 Nov 2008
You will probably see more questions involving triangles than any other part of geometry in the GMAT so pay attention to these next few pages.
Basic Triangle Facts
Angles
The sum of the angles in a triangle is always 180°.
In this triangle below x + y + z = 180.
Area
The area of a triangle is , where the height is the perpendicular distance from the base to the top of the triangle.
Triangle Inequality
The triangle inequality says that no one side of a triangle can be longer than or equal to the sum of the other two.
The reason for this is fairly obvious when you think about it because if one side is longer than or equal to the sum of the other two then you cannot join the two shorter sides to form a triangle.
Therefore, if we have a triangle with sides of length r, s and t.
We can write down the following inequalities.
Types of Triangles
- Isosceles triangle
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An isosceles triangle is a triangle where two of the sides are equal, and two of the angles are equal.
- Equilateral triangle
An equilateral triangle is a triangle where all three sides are equal, and all three angles are equal.
You should be able to see that since the angles sum to 180°, each angle must be 60°.
- Right-angled triangle
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A right-angled triangle is a triangle with one right angle in it.
I leave it as an exercise for you to work out why a triangle cannot have two right angles. We will see why right-angled triangles are so important next.
