Geometric Relationships
Geometry: The branch of math that defines and relates the basic properties and measurement of line segments and angles.
Set: A collection of objects such that it is possible to determine whether a given object belongs to the collection or not
Point: has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, ( x,y ).
Line: has no thickness but its length extends in one dimension and goes on forever in both directions. Unless otherwise stated a line is drawn as a straight line with two arrowheads indicating that the line extends without end in both directions. A line is named by a single lowercase letter, l , or by any two points on the line,
Plane: has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or a parallelogram. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m ) or by three noncollinear points (plane ABC).

Simple Geometric Terms:
Ray: Part of a line that consists of a point on the line (called the endpoint) and all the points on one side of the endpoint.
Opposite Rays: Two rays of the same line with a common endpoint and no other point in common.
Line Segments or Segment: A set of points consisting of two points on a line
(called the endpoints) and all of the points on the line between the endpoints
Midpoint of a Line Segment: A point of that line segment that divides the segment into two congruent segments.
Parallel Lines: Two lines in the same plane that never intersect.
Perpendicular Lines: Two lines in the same plane that intersect to form right angles
Skew Lines: Two lines in space that are neither parallel nor perpendicular (will never be in the same plane)
Collinear Points: Points in a plane, on the same line
Coplanar Points: A set of all points lying in the same plane
Non-Collinear Points: Points in a plane, not on the same line
Dihedral Angle: created by the union of two half planes with a common edge.

Relationships Between:
Points and Lines
A point may be on a line
A point may not be on a line
Points and Planes
A point may be in a plane
A point may not be in a plane
Lines and Planes
A line may be in a plane
A line may intersect a plane at a single point
A line may not intersect a plane at all (considered parallel to the plane)
Planes and Planes
A plane may be in a plane, intersection is plane itself
A plane may intersect a plane, intersection is line
A plane may not intersect a plane (parallel planes)
What Determines a Plane:
Three non collinear points
A line and a point not on the line
Two intersecting lines
Two parallel lines

Problems Involving Points/Lines/Planes
1) In this rectangular sided box
(a) List three pairs of lines that lie in the same plane?
(b) Plane GHB and EFC are (circle one): a) Parallel b) Perpendicular c) Neither
(c) True/False: Points F, C and B are coplanar.
(d) True/False: Points G, A and D are coplanar.
(e) True/False: Points F, D and H are coplanar.
(f) List three pairs of lines that are coplanar.
(g) List three pairs of lines that are skew.
2) True/False: When two planes intersect, two lines are formed.
3) True/False: Only one plane contains two intersecting lines.
4) True/False: If two points lie in a plane, the line joining them also lies in the same plane.

5) In this rectangular sided box:
(a) For this rectangular solid, which plane(s) contain D and are parallel to plane FEG ?
(Circle one) a) Planes DAB and GAD b) Planes DCB and FCB c) Only plane DAB.
(b)
(c)
(d)
True/False:
True/False:
True/False:
Points H, B and C are all collinear.
Plane EDA and Plane FCD are parallel.
Plane FEG and Plane CBH are perpendicular.
(e) True/False: Lines FC and GA are coplanar
(f) For this rectangular solid, which plane(s) contain H and are perpendicular to plane DCB? (Circle one) a) Planes FCB and GAB b) Planes EGA and GHB
6) True/False: There is more then one plane which contains three points in space.

7) In the following triangular prism below:
(a)
(b)
List three pair of skew lines.
Plane ACB and Plane ________ are parallel.
(c) True/False: AC and DE are perpendicular.
8) Two planes which intersect from _______________.
9) At a given point on a line, there are ( 1 , a few, infinitely many) lines perpendicular to the given line. (Circle correct answer)
10) If a line not in a plane intersects the plane, then it intersects in (1, a few, infinitely many) place(s). (Circle the correct answer)
11) True/False: You must have at least three intersecting lines to determine a plane