Geometry: A Mathematical System

Space is...

• the set of all possible points

• a set of two or more points all on the same line

• a set of two or more points all on the same plane

• point B is between A and C if A, B, and C are collinear and the equation, AB+BC=AC is true, where AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively

Collinear points are...

• the set of all possible points

• a set of two or more points all on the same line

• a set of two or more points all on the same plane

• point B is between A and C if A, B, and C are collinear and the equation, AB+BC=AC is true, where AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively

Coplanar points are...

• the set of all posible points

• a set of two or more points all on the same line

• a set of two or more points all on the same plane

• point B is between A and C if A, B, and C are collinear and the equation, AB+BC=AC is true, where AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively

The betweeness of points is...

• the set of all possible points

• a set of two or more points all on the same line

• a set of two or more points all on the same plane

• point B is between A and C if A, B, and C are collinear and the equation, AB+BC=AC is true, where AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively

A line segment is...

• the set of two different points and all the points between them

• the distance between the end points of a segment

• the point on a segment that divides the segment into two equal segments

• a line or segment that intersects the segment at its midpoint

The length of a segment is...

• the distance between the endpoints of a segment

• the point on a segment that divides the segment into two equal segments

• a line or segment that intersects the segment at its midpoint

• a ray, AC, with endpoint A and containing a second point C, is the set of points on AC and all points such that C is between them and A

The midpoint of a segment is...

• the point on a segment that divides the segment into two equal segments

• a line or segment that intersects the segment at its midpoint

• a ray, AC, with endpoint A and containing a second point C, is the set of points on AC and all points such that C is between them and A

• BA and BC are opposite rays if A, B, and C are collinear and B (the endpoint of both rays) is between A and C

The bisector of a segment is...

• a line or segment that intersects the segment at its midpoint

• a ray, AC, with endpoint A and containing a second point C, is the set of points on AC and all points such that C is between them and A

• BA and BC are opposite rays if A, B, and C are collinear and B (the end point of both rays) is between A and C

• the set of two different points and all points between them

A ray is...

• a ray, AC, with endpoint A and containing a second point C, is the set of points on AC and all points such that C is between them and A

• BA and BC are opposite rays if A, B, and C are collinear and B (the end point of both rays) is between A and C

• the set of two different points and all the points between them

• the distance between the endpoints of a segment

Opposite rays are...

• BA and BC are opposite rays if A, B, and C are collinear and B (the end point of both rays) is between A and C

• the set of two different points and all the points between them

• the distance between the endpoints of a segment

• the point on a segment that divides the segment into two equal segments