Chapter 1 - Geometry

Point

A location, such as a dot on a map or on a computer

Line

An infinite set of points - straightness, suggested by a string of small dots

Plane

An infinite set of points - flatness extending in all directions

Space

The set of all points

Collinear points

points that all lie on the same line

Coplanar Points

Points that lie on the same plane

Intersection

Of two figures, it is the set of points that both figures have in common

Postulate

A statement that is accepted as a true without proof.

Postulate 1 - Ruler Postulate

Points in a line can be matched 1:1 with real numbers. The real number that corresponds to a point is the coordinate of the point.

Postulate 2: Segment Addition Postulate

If B is between A and C, then AB + BC = AC, if AB + BC = AC then B is between A and C.

Congruent Segments

Segments that have the same length

Midpoint of a Segment

The point that divides the segment into two congruent segments

Angle

Consists of two different rays that have the same initial points

Sides of the angle

Rays

Vertex of the angle

Initial point

Degrees

The unit that angles are measured in

Congruent Angles

Angles that are equal in measure

Acute Angles

An angle measure between 0 and 90 degrees.

Right Angles

An angle that is exactly 90 degrees

Obtuse Angle

An angle greater than 90 degrees and less than 180

Straight Angle

An angle that is exactly 180 degrees

Postulate 4 - Angle Addition Postulate

If point B lies in the interior of angle AOC, then m<AOB + m<BOC = m<AOC

If <AOC is a straight angle and B is any point not on AC, then m<AOB + m<BOC = 180

Adjacent Angles

Two angles are adjacent angles if they share a common vertex and side, but have no common interior points.

Postulate

A line contains at least 2 points; a plane contains at least 3 points not all in one line; space contains at least four points nit all in one plane

Postulate

Through any 2 points, there is exactly one line

Postulate

Through any 3 points there is at least one plane, and through any 3 noncollinear points there is exactly one plane.

Postulate

If two points are in a plane, then the line that contains the points is in that plane

Postulate

If two points are in a plane, then the line that contains the points is in that plane

Postulate

If two planes intersect, then their intersection is a line

Theorem

If two lines intersect, then they intersect in exactly one point

Theorem

Through a line and a point not in the line, there is exactly one plane

Theorem

If two lines intersect. then exactly one plane contains the line

One and only one means…

exactly one

Exists means…

at least one

Unique means..

No more than one