I this section many of the theorems of angles and triangles are discussed. You will find these theorems to be very useful when applied to physics concepts.

Certain things must be true in order for two angles to be equal.

The first is two angles are equal if they are vertical angles.
Two angles are equal if the left side of one angle is parallel to the left side of the other angle and the right side of the same angle is parallel to the right side of the other angle.
Two angles are equal if the left side of one angle is perpendicular to the left side of the other angle and the right side of the first angle is perpendicular to the right side of the second angle.

The sum of the 3 inner angles of any triangle is always 180°
Similar triangles are two triangles where all 3 of there inner angles are equal. Similar triangles do not necessarily have the same side lengths.
The 2 theorems that define similar triangles are:
  • Similar triangles require the measure of their angles to be the same.
  • The sides of the triangles fit into the ratio below.
Congruent Triangles are 2 similar triangles with corresponding sides of equal length.

In order for two triangles to be congruent they must fit one of the descriptions below:

  • The 3 corresponding sides are equal.
  • 2 sides and the enclosed angle are equal
  • 2 angles and the enclosed side are equal

There are simple ways to remember these 3 theorems.

  • Side - Side - Side or SSS
  • Side - Angle - Side or SAS
  • Angle - Side - Angle or ASA

There are three types of triangles. The first are right triangles. A right triangle is a triangle with one of its angles equal to 90° (a right angle). The other 2 angles will add up to 90° so that all three inner angles total 180°.

The next type of triangle is the Isosceles triangle. An Isosceles triangle is defined as a triangle with 2 angles of equal measure. A triangle could be both a right triangle and an Isosceles triangle.

Equilateral triangles are the third type of triangle. The equilateral triangle has all 3 of its sides equal in length. As a result each of the inner angles will always be equal to 60° totaling 180°.

The Pythagorean Theorem is one of the most used theorems in geometry. It is so useful because by knowing any two sides of a right triangle you can find the 3rd. The theorem, developed by a famous Greek mathematician Pythagorous, is defined as the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the other two sides.

There are two other important laws which define triangles:
The Law of Sines and The Law of Cosines
described in the trigonometry section.