chapter 1 terms and defintions

Point

A point has no dimension and is represented by a dot.

Line

A line has one dimension and is represented by a line with two arrowheads, extending without end.

Plane

A plane has two dimensions; through any three noncollinear points, there is exactly one plane.

Collinear Points

Points that lie on the same line.

Coplanar

Points that lie on the same plane.

Segment

A segment is part of a line that consists of two endpoints and all points in between.

Ray

A ray is part of a line consisting of one endpoint and all other points on one side of the endpoint.

Opposite Rays

Two rays that share the same endpoint and form a line.

Intersection

Two or more geometric figures intersect if they have one or more points in common.

Ruler Postulate

Every point on a line can be paired with a real number, establishing a one-to-one correspondence between points and real numbers.

Distance

The distance between two points A and B is the absolute value of the difference of their coordinates.

Segment Addition Postulate

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

Congruent Segments

Segments that have the same length.

Midpoint

The midpoint of a segment divides the segment into two equal segments.

Midpoint Formula

The midpoint M of segment AB with endpoints A(x1, y1) and B(x2, y2) is M((x1 + x2)/2 , (y1 + y2)/2).

Segment Bisector

A point, line, ray, or segment that cuts another segment in half at its midpoint.

Distance Formula

The distance d between points A(x1, y1) and B(x2, y2) is d = √((x2 - x1)² + (y2 - y1)²).

Angle

An angle is formed by two rays with the same endpoint.

Sides of an Angle

The rays of an angle.

Vertex of an Angle

The endpoint of an angle.

Acute Angle

An angle that measures less than 90 degrees.

Right Angle

An angle that measures exactly 90 degrees.

Obtuse Angle

An angle that measures greater than 90 degrees and less than 180 degrees.

Straight Angle

An angle that measures exactly 180 degrees.

Angle Addition Postulate

If a point is in the interior of an angle, then the two smaller angles will sum to the larger angle.

Complementary Angles

Two angles whose measures sum to 90 degrees.

Supplementary Angles

Two angles whose measures sum to 180 degrees.

Adjacent Angles

Angles that share a common side.

Linear Pair

Two adjacent angles whose uncommon sides are opposite rays.