Geometry Chapter 3: Triangles

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While there are many different kinds of triangles, there are some rules that are specific to all triangles, and we will start with these. Figure 1, below, is a generic triangle. If you draw different kinds of triangles, these rules will always hold true.

1. The angles of any triangle will ALWAYS add up to 180°. For the three internal angles of a triangle: x° + y° + z° = 180°.       2. The biggest side is ALWAYS opposite the biggest angle and the smallest side is ALWAYS opposite the smallest angle. In this case, we can therefore see x must be the smallest angle, because it is opposite side A, which is the smallest side.         3. Any side of a triangle will always be less than the sum of the other two sides but greater than the difference of the other two sides. In Figure 1, if we take side C, for example, we can say (B – A) < C < (B + A).           4. If we draw an external line, as in Figure 2, the angle formed will always be equal to the sum of the other two angles in the triangle. In this case, n = x + y. That is because x + y + z = 180 and n + z = 180. Therefore n must equal x + y. This property will be true for any triangle

Perimeter and Area

The perimeter of any figure is the distance around the outside of the figure, or the sum of the sides of that figure. The perimeter in Figure 1 is A + B + C.

The area of any figure is the amount of space that is inside that figure. Each figure has a different formula for finding its area.

To find the area of a triangle, we always need two elements: the base and the height.

The base of any triangle can be any of its sides. The height of the triangle is the perpendicular distance from the base to the opposite angle. Here are some examples of triangles with different bases and heights.

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Contents of Geometry Chapter: Table of Contents Chapter 1: Angles and Lines   Chapter 2: Intersecting Angles   Chapter 3: Triangles   Chapter 4: Circles   Chapter 5: Perimeters & Areas   Chapter 6: Solids   Chapter 7: Coordinate Geometry    Chapter 4: Circles

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