Idiot\'s Guides Basic Math and Pre-Algebra

168 Part 3: The Shape of the World

In most triangles, the altitude, the angle bisector, and the median from a vertex are all different

line segments.

It’s often the case that something is true only for some triangles, but there are things that are true

about any triangle. One important one is called the Triangle Sum theorem. In any triangle, the

sum of the measures of the three angles is 180r. You can see this if you cut a triangle out of paper

and tear off two corners and set them next to the third corner.

The torn corners can be put together to form a 180r angle.

If 'ABC is a triangle with ’B = 90r, the sum of the measures of ’A and ’C must be 90r because

the three angles of the triangle total 180r. If ’B measures 90r, the other two angles must make up

the other 90r.

An exterior angle of a triangle is formed by extending one side of the triangle. The measure of an

exterior angle of a triangle is equal to the sum of the two remote interior angles.

DEFINITION

If one side of a triangle is extended, the adjacent angle formed is called an exterior

angle of the triangle.

The sum of the two remote interior angles (m’1 and m’2) equals the measure of the exterior angle (m’3):

m’1 + m’2 = m’3.

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