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Geometry Vocabulary #1:
Undefined terms - term that is used without a specific mathematical definition.
1) Point - location
- no size
- represented by a small dot and with capital letter
Example:
2) Line - set of points that extends in 2 opposite directions without end.
- 2 points name a line (in any order) or single lowercase letter
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3) Plane - set of points that extends along a flat surface in every direction without end.
- named by any three points of the plane that do not lie on the same line, or
single capital letter.
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Definition - statement of the meaning of a word or phrase.
Fundamental Definitions Related to Points:
1) Space - the set of all points.
2) Figure - any set of points.
A) Plane Figure - if points all lie in the same plane
B) Space Figure (3-D Figure) - if a figure extends beyond a single plane into
space
3) Intersection - the set of all points common to two or more figures.
4) Collinear Points - points that lie on the same line.
Noncollincar points - points that do not lie on the same line.
5) Coplanar Figures - figures that lie on the same plane.
Noncoplanar figures - figures that do not lie on the same plane.
Postulate - the truth of some statements are accepted without proof.
Basic Postulates for Points, Lines. & Planes:
1) Unique Line Postulate - through any two points is exactly 1 line.
2) Line Intersection Postulate - if 2 lines intersect, then they intersect in exactly one
point.
3) Plane Intersection Postulate - through any 3 noncollinear points there is exactly 1
plane.
Definitions Related to Segments:
1) Line Segment (segment) - part of a line that begins at 1 point and ends at another.
Example:
2) Length of a Segment - distance between its endpoints.
3) Congruent Segments - segments that are equal in length, symbol is
Example:
4) Midpoint - point that divides the segment into 2 congruent segments.
Simplified:
Example:
Segment Addition Postulate - if point C is between point A and point B, then AC + CB = AB.
Example:
Geometry Vocabulary #2:
Definitions Related to Rays:
1) Ray - part of a line that begins at 1 point & extends without end in one
direction.
- named by its endpoint & one other point on it.
Example:
2) Endpoint of the ray - point at which ray extends from.
3) Opposite Rays - on a line, if point B is between point A & point C, then BA &
BC are
opposite rays
Example:
4) Angle - figure formed by 2 rays with a common endpoint.
- each ray is the side of the angle, the endpoint is the vertex of the angle.
Examples:
Definitions Related to Angle Measure:
1) Congruent Angles - angles that are equal in measure.
Example:
2) Acute angle - angle whose measure is greater than 0 degrees & less than 90
degrees.
Example:
180
3) Obtuse angle - angle whose measure is greater than 90 degrees & less than
degrees.
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4) Right Angle - angle whose measure is 90 degrees.
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5) Straight Angle - angle whose measure is 180 degrees.
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6) Complementary Angles - 2 angles whose measure have a sum of 90 degrees
- each angle is said to be the complement of the
other.
Example:
7) Supplementary angles - 2 angles whose measures have a sum of 180 degree
- each angle is said to be the supplement of the other
Example:
Adjacent angles - 2 coplanar angles that share a common side & a common vertex, bu1
have no interior points in common.
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Linear Pair - when the uncommon sides of 2 adjacent angles are opposite rays.
Example:
Linear Pair Postulate - if 2 angles form a linear pair, then they are supplementary.
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Geometry Vocabulary #3:
Vertical angles - 2 angles whose sides form two pairs of opposite rays.
Example:
Theorem - statement that can be proved true.
Vertical Angles Theorem - 2 angles are vertical angles, then they are congruent
Example:
Perpendicular Lines - 2 lines that intersect to form right angles.
- symbol is
.
Example:
Parallel Lines - coplanar lines that do not intersect.
- symbol is
.
Example:
Skew Lines - noncoplanar lines
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