| A | B |
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| AXES | A reference line used in a graph or coordinate system. |
| X-AXIS | The horizontal number line in the coordinate system. |
| Y-AXIS | (Black Line) --The vertical number line in the coordinate system. |
| ORIGIN | (Blue Point) -- A fixed point from which measurements are taken. The origin (Point O) has coordinates (0,0) and is found at the point of intersection between the x-axis and the y-axis. |
| QUADRANT -- | One of the four regions formed by the intersection of the x-axis and the y-axis. Quadrant I - all points (+,+), Quadrant II - all points (-,+), Quadrant III - all points (-,-), Quadrant IV - all points (+,-) |
| ORDERED PAIR -- | A pair of numbers (x coordinate, y coordinate) indicating the position of a point in the Cartesian Plane, for example P(6,3), a positive 6 x-value and a positive 3 y-value. |
| COLLINEAR POINTS -- | Points which lie on a straight line. Any two points are collinear because there is a straight line that passes through both. Thus we often determine if three points are collinear. Example: Points A, B and C are collinear. |
| NON COLLINEAR POINTS -- | Opposite of Collinear Points - Points that do not lie on the same line. Example: Points A, B and D are non-collinear. |
| Determining Collinearity | For a point to be on a line it must 'satisfy' or solve the equation. For example, the equation y = 2x + 3 describes a line. If a point lies on this line then it will balance the equation. |
| A POINT | is one of the basic UNDEFINED terms of geometry. They have no length, width, or thickness and we often use a dot to represent it. The diagram gives examples of some of the possible |
| A Line | is one of the basic UNDEFINED terms of geometry. A line has no thickness but its length goes on forever in two directions. The diagram gives examples of some of the possible |
| COPLANAR POINTS -- | Points that lie in the same plane. Points A, B, & C are coplanar. All points plotted in the Cartesian Plane are coplanar. |
| NOT COPLANAR POINTS -- | The Point D does not lie in Plane ABC, thus the Point D is not coplanar with A, B & C. The Points B, C & D define a new Plane BCD. The Points A, B & D define a new Plane ABD. The Points A, C & D define a new Plane ACD. |
| THE INTERSECTION OF TWO PLANES | The intersection of two unique planes is a line. |
| Planes | are often modeled by flat surfaces such as window panes or walls. Unlike these surfaces, a plane has no thickness and extends indefinitely in all directions and are often represented or modeled using four sided-figures like the one to the left. A plane is defined and named by three noncollinear points, thus this could be called Plane ABC |
| DEFINITION OF BETWEENESS - | In the figure, Point B is between A and C while Point H is not between A and B. For B to be between A and C, all three points must be collinear and B must lie on segment AC. |
| A POSTULATE | is a statement that is assumed to be true. |
| A POSTULATE | is an initial proposition or statement that is accepted as true without proof and from which further statements, or theorems, can be derived. |
| Postulate 1-1 The Ruler Postulate | The points on any line can be paired with the real numbers so that given any two points P and Q on the line, P corresponds to zero, and Q corresponds to a positive number. |
| Postulate 1-2 Segment Addition Postulate | If R is between P and Q, then PR + RQ = PQ. If PR + RQ = PQ, then R is between P and Q. |
| The Distance Formula: | Distances can be determined on both a number line and in the Coordinate Plane. A NUMBER LINE is a straight horizontal line on which each point represents a real number. Integers are points marked at unit distance apart (....-3,-2,-1,0,1,2,3,...) as shown below. |
| CONGRUENT SEGMENTS | Segments that are equal in length are called |
| Theorem 1-1 Midpoint Theorem | If M is the midpoint of AB then AM = MB |
| SEGMENT BISECTOR. | Any segment, line, or plane that intersects a segment at its midpoint is called a SEGMENT BISECTOR. |
| ANGLE | - An angle is formed by two rays which begin at the same point (if the two rays lie on the same line, then it is called a straight angle). |
| VERTEX - | The common point for both rays is called the Vertex. |
| Postulate 1-3 Protractor Postulate | Given AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on each side of , such that the measure of the angle formed is r. |
| Postulate 1-4 Angle Addition Postulate | If R is in the interior of PQS, then PQR + RQS = PQS. If angle PQR +angle PQS = angle PQS then R is the interior of PQS |
| An ACUTE ANGLE | is one whose measure is LESS THAN 90 DEGREES. Notice CAB does not quite reach 90 degrees... acute angles are always less than 90 degrees. |
| Right Angles | A RIGHT ANGLE is an angle whose measure is EXACTLY 90 DEGRRES. Right angles are denoted by a small square in its interior. |
| Straight Angles | A STRAIGHT ANGLE is one whose measure is EXACTLY 180 DEGREES. A straight angle is made up of two opposite rays. Another important fact is that a straight angle forms a straight line. This information will be used very frequently throughout the year. |
| Reflex Angle | A REFLEX ANGLE is one whose measure is GREATER THAN 180 AND LESS THAN 360 DEGREES. |
| Congruent Angle | CONGRUENT ANGLES - Two angles that have the same measure are called Congruent Angles. Equal measure angles are labeled as shown in the diagram. |
| ANGLE BISECTOR - | For ray QR to be the angle bisector of angle PQS, point R must be on the interior of angle PQS and angle PQR must be congruent to angle RQS |
| ADJACENT ANGLES | are angles in the same plane, that have a common vertex and a common side, but no common interior points. In the diagram HKF and FKI share vertex K and side KF. |
| Vertical Angles | are two nonadjacent angles formed by two intersecting lines. (These can be found by the X that the two intersecting lines form) |
| Linear Pair | of angles are adjacent angles who non common sides are oppposite rays. The sum of the measures of the angles in a linear pair is 180. |
| Supplementary Angles | If the sum of the measures of two angles is 180 degrees, then the angles are supplementary. (One angle is the supplement of the other.) |
| Complementary Angles | If the sum of the measures of two angles is 90 degrees, then the angles are complementary. (One angle is the complement of the other.) |
| Perpendicular Lines: | re two lines that intersect to form a right angle. |
