Triangles and their properties

We show different properties of triangles.

Height of a triangle

The height is the line going from one point of the triangle to the opposite side such that the line and the side are perpendicular. The height of a is the line from the side a to the point A which is opposite of it. The heights of a triangle all meet in one point.

triangle-height

In some cases the meeting point of the heights will be outside of the triangle and the sides will have to be extended to find the point where the height intersects the side with a right angle.

triangle-height2

Area of a triangle

A right triangle can be duplicated and mirrored to get a rectangle.

triangle-area

The area of the rectangle is equation and because it is twice as big as the triangle, we only need to divide it by 2 to find the area of the triangle: equation.

If the triangle is not a right triangle, we can use its height to divide it into two right triangles. This makes calculating the area easy for us because we already know how to calculate it of a right triangle.

triangle-area2

In this case, we use the height on side c. Let us call the left side of c to the left of the height equation and the right side equation. We can calculate the area as follows:

    equation

In this example we used side c. In general we can use any side and the side that we choose is called the base side b. So in general we calculate the area with the base side b and height h as follows:

    equation

Angle bisectors of triangles

The ange bisector is the line that divides an angle equally. The intersection point of all angle bisectors is always inside the triangle and is called in incenter.

triangle-bisector