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Prentice Hall California definitions and postulates

### Inductive Reasoning

A type of reasoning that reaches conclusions based on a pattern of specific examples or past events.

### Plane

A flat surface that has no thickness. Contains many lines and extends without end in the directions of its lines.

### Postulate 1.2 "If two lines intersect..."

If two lines intersect, then they intersect at exactly one point.

### Postulate 1.3 "If two planes intersect..."

If two planes intersect, then they intersect in exactly one line.

### Postulate 1.4 "Through any three..."

Through any three noncollinear points there is exactly one plane.

### Segment

The part of a line consisting of two points, called endpoints and all the points between them.

### Ray

The part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.

### Ruler Postulate

The points of a line can be put into a one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.

### Coordinate

The distance and direction from the origin of a number line. The coordinates of a point on a coordinate plane are in the form where x is the x-coordinate and y is the y-coordinate.

### Segment Addition Postulate

If three points, A, B, and C are collinear and B is between A and C, then AB + BC = AC.

### Protractor Postulate

Let ray OA and ray OB be opposite rays in a plane. Ray OA, ray OB, and all rays with endpoint O that can be drawn on one side of line AB can be paired with the real numbers from 0 to 180 so that:

a. ray OA is paired with 0 and ray OB is paired with 180.

b. If ray OC is paired with x and ray ODis paired with y, then the measure of angle COD = |x-y|.

### Angle

Formed by two rays with the same endpoint. The rays are the sides of the angle and with the common endpoint is the vertex of the angle.

### Adjacent Angles

Two coplanar angles that have a common side and a common vertex but no common interior points

### Perpendicular Bisector

A line, segment, or ray that is perpendicular to the segment at its midpoint.