September 24, 2010

Foundations of

Important Vocabulary

Undefined Terms: a term that is used without a specific example or description. We use these terms to describe other terms in geometry. 1) : a location. A point has neither shape nor size. When we name a point, we name it by a capital letter.

Example: W

2) : made up of points and has no thickness or width. There is exactly one line through any two points. A line can either be named by two points on that line or a lowercase script letter.

Example: k X Y

3) Plane: a flat surface that extends indefinitely in all directions. There is exactly one plane through any three points that are not on the same line. A plane is named by a capital script letter or by any three points on that plane.

Example: A

W X Y September 24, 2010 Fundamental Definitions in Geometry Definitions Related to Points:

· Space: the set of all points.

· Figure: any set of points. · Plane Figure: all points lie on the same plane. · Space Figure: a 3-D figure, sketched beyond the plane. · Intersection: the set of all points common to two or more figures.

· Collinear Points: points that lie on the same line.

· Non-Collinear Points: points that do not lie on the same line.

· Coplanar Figures: figures that lie on the same plane.

· Non-Coplanar Figures: figues that do not lie on the same plane.

Definitions Related to Line Segments:

1) (segment): a part of a line that begins at one point and ends at another.

Example: A B 2) Length of a Segment: distance of a segment between its two endpoints.

3) Congruent Segments: segments that have the same exact distance. 5 cm Example: A B 5 cm C D

4) Midpoint: divides a segment into two congruent segments. 2 in 2 in Example: C M D September 24, 2010 Basic Postulates for Points, Lines, and Planes

Postulates: statements that are considered true, even without proof.

· Unique Line Postulate: through any two points is exactly one line.

· Line Intersection Postulate: if lines intersect, then they intersect in exactly one point.

· Plane Intersection Postulate: through any three non-collinear points, there is exactly one plane.

Definitions Related to Rays

1) Ray: a part of a line that begins at one point and extends infinitely (without end) in one direction. We name a ray by its endpoint and one other point on that ray.

Example: A

J 2) Endpoint of a Ray: the point at which the ray extends from.

3) Opposite Rays: two rays that meet together to form a line. Opposite rays share a common endpoint and extend in opposite directions.

Example: A B C

4) : a figure formed by two rays with a common endpoint. Each ray is the side of the angle and each endpoint is thevertex of the angle. ***A vertex of an angle is the place where the two sides of the angle meet*** W Example: X Y September 24, 2010

Definitions Related to Angle Measure

1) Congruent : Angles that are equal in measure. A Example: T

C E O M 2) Acute Angle: an angle whose measure is greater than 0 degrees, but less than 90 degrees.

Example: L

Y N 3) Obtuse Angle: an angle whose measure is greater than 90 degrees, but less than 180 degrees.

Example: N V I 4) : an angle whose measure is exactly 90 degrees.

O Example: M

A

5) Straight Angle: an angle whose measure is exactly 180 degrees.

Example:

P A T

Angle Pairs 1) Complementary Angles: Two angles whose measure has a sum of 90 degrees. Each angle is said to be the complement of each other.

Example: Q T

R S 2) Supplementary Angles: Two angles whose measure has a sum of 180 degrees. Each angle is said to be thesupplement of each other.

Example: W

D R E

3) Adjacent Angles: Two coplanar angles that share a common side and a comment vertex, but have no interior points.

Example: N K ο 51 ο 28 I C 4) Linear Pair: When the two uncommon sides of adjacent angles are opposite rays. A linear pair creates a line.

Example: Y

A N D

5) Linear Pair Postulate: If two angles form a linear pair, then they are supplementary.

6) Vertical Angles: Two angles that are directly opposite each other. A pair of vertical angles are congruent.

Examples: S T E

P H September 24, 2010 Different Types of Lines

1) Parallel Lines: coplanar lines that never intersect. The symbol for parallel lines is: ||

Example: k

l

2) Lines: coplanar lines that intersect to form right angles. The symbol for perpendicular lines is: ┴ m Example:

h

3) Skew Lines: lines that are not on the same plane.

Example: