| Term | Definition |
|---|
| Ray | In which AB is the set of points, A, B, and all points X, such that either A-X-B or A-B-X |
| Angle | An angle is a pair of rays that have the same endpoint |
| Vertex | The common endpoint of the two rays that make up an angle |
| Sides | The rays that make up an angle |
| Opposite Rays | Rays AB and AC are _______ ___ iff B-A-C |
| Linear Pair | ...iff they have a common side and their other sides are opposite rays |
| Vertical Angles | ...iff the sides of one angle are opposite rays to the sides of the other angle |
| Degree | The unit used to measure angles in geometry (based on 360) |
| Protractor | The instument used to measure angles; 180° |
| Protractor Postulate; The rays in a half-rotation can be numbered so that: | A) ...to every ray there corresponds exactly one real number called its coordinate. B) ...to every real number from 0 to 180 inclusive, there corresponds exactly one ray. C) ...to every pair of rays there corresponds exactly one real number called the measure of the angle that they determine. D) ...the measure of an angle is the absolute value of the difference between the coordinates of its rays |
| Acute Angle | An angle that's measure is LESS than 90° |
| Right Angle | An angle that's measure is 90° |
| Obtuse Angle | An angle that's measure is GREATER than 90° |
| Straight Angle | An angle that's measure is 180° |
| Minute | 1/60th of a degree. |
| Second | 1/60th of a minute. |
| Betweenness of Rays (Definition) | Suppose that OA, OB, and OC are in a half-rotation with coordinates a,b, and c respectively. OB is between OA and OC (OA-OB-OC) iff either a〈b〈c or c〉b〉a. |
| Betweenness of Rays Theorem; If OA-OB-OC, | then angle AOB + angle BOC = angle AOC |
| Ray Bisects an Angle (Definition) | ...iff it is between the sides of the angle and divides it into two equal angles. |
| Angle Bisector Theorem | A ray that bisects an angle divides it into angles half as large as the angle. |
| Complementary Angles | ...iff the sum of their measures is 90°. |
| Supplementary | ...iff the sum of their measures is 180°. |
| (Theorem 5A) Complements of the same angle... | are equal. |
| (Theorem 5B) Complements of equal angles... | are equal |
| Supplements of the same angle... | are equal |
| Supplements of equal angles.. | are equal |
| (Theorem 7) If two angles are a linear pair | ... then they are supplementary. |
| (Theorem 8) If 2 angles in a linear pair are equal | ... then each is a right angle. |
| (Theorem 9) If two angles are vertical angles | ...then they are equal. |
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