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Angles can be classified by their measure:
Right angles are angles that measure 90°. It is often indicated by a square.
Acute angles are angles that measure between 0 and 90°.
Obtuse angles are angles that measure between 90 and 180°.
Straight angles are angles that measure 180°.
Postulate: The Protractor Postulate
Given line AB and a point O on line AB. Consider rays OA and OB, as well as all the other rays that can be drawn, with O as an endpoint, on one side of line AB. These rays can be paired with the real numbers between 0 and 180 in such a way that:
  1. Ray OA is paired with 0, and ray OB is paired with 180.
Angles are geometric figures formed by two rays having the same endpoint. The two rays are called the sides of the angle, and their common endpoint the vertex of the angle.
Angles
Theorem:
he Midpoint Theorem: ( The Definition of Midpoint)
Given AB, its midpoint M is:
2AM = AB and AM = ½ AB
2MB = AB and MB = ½ AB
A perpendicular bisector of a segment is a line, ray or another segment that is perpendicular to the segment at its midpoint.
Theorem:
Postulate: Segment Addition Postulate
Point B is a point on segment AC, i.e. B is between A and C, if and only if
AB + BC = AC
Postulate: The Ruler Postulate
The points on any line can be paired with the real numbers in such a way that:
  1. Any two chosen points can be paired with 0 and 1.
  2. The distance between any two points in a number line is the absolute. value of the difference of the real numbers corresponding to the points.
Consider the line:
Point B is between points A and C, and A, B and C are collinear.
Segment AC consists of points A and C and all points in between A and C. Points A and C are called the endpoints of the segment AC.Â
Segments and Rays
Proofs
Postulates are statements that are assumed to be true especially in arguments.
Theorems are propositions that need to be proven first before it can be used in a proof.
Postulates and Theorems are used to prove geometric ideas.
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