Term
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Definition
The set of all points
Pg. 6 |
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Term
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Definition
Points all in one line
Pg. 6 |
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Term
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Definition
Points all in one plane
Pg. 6 |
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Term
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Definition
Where two figures(lines, planes, or the combination
of both) meet or cut.
The set of points that are in both figures. Pg. 6 |
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Term
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Definition
Shown by two letters(the endpoints) with a
line over it.
Constists of the endpoints and all points between
those endpoints. Pg. 11 |
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Term
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Definition
Shown by two letters(one an endpoint named first and another) with an arrow going to the right over the top.
Consists of the endpoint and all points to and paste the second letter. Pg. 11 |
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Term
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Definition
Rays that start at the same endpoint, but go
in opposite direction. Pg. 11 |
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Term
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Definition
Shown by two letters(the endpoints).
Subtract the coordinates of it endpoints. Pg. 11 |
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Term
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Definition
Statements that are accepted wihout proof
Pg. 12 |
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Term
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Definition
1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinantes 0 and 1.
2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates. Pg. 12 |
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Term
Segment Addition
Postulate |
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Definition
If B is between A and C, then
AB + BC = AC
PG. 12 |
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Term
Congruent and
Congruent Segments |
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Definition
Two objects that have the same size and shape.
Two segements that have equal length.
Pg. 13 |
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Term
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Definition
The point that divides the segment into two congruent segements.
Pg. 13 |
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Term
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Definition
A line, segment, ray, or plane that intersects the segment at its midpoint.
Pg. 13 |
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Term
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Definition
The figure formed by two rays that have the same endpoint.
Pg. 17 |
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Term
Sides &Vertex
of an angle |
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Definition
Sides - the two rays that form the angle
Vertex - the common endpoint of the rays that form the angle
Pg. 17 |
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Term
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Definition
Measure between o and 90
Pg. 17 |
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Term
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Definition
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Term
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Definition
Measure between 90 and 180
Pg. 17 |
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Term
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Definition
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Term
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Definition
On line AB in a given plane, choose any point 0 between A and B. Consider line OA and line OB and all the rays that can be drawn from o on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that:
a. Line OA is paired with 0, and line OB with 180.
b. If line OB is paired with x, and line OQ with y, then m ‹ POQ = ǀx-yǀ Pg. 18 |
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Term
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Definition
If point B lines in the interior of <AOC, then
m< AOB + m< BOC = m< AOC
If < AOC is a straight angle and B is any point not on line AC, then
m< AOC + m< BOC = 180 Pg. 18 |
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Term
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Definition
Angles that have equal measures
Pg. 19 |
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Term
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Definition
Two angles in a plane that have a common vertex and a common side but no common interior points
Pg. 19 |
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Term
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Definition
The ray that divides that angle inot two congruent adjacent angles.
Pg. 19 |
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Term
Postulate 5
# of points in a line |
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Definition
A Line contains at least two points; a plane contains at least three points not all in one line; space contaoins at least four points not all in one plane.
Pg. 23 |
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Term
Postulate 6
Forming a line |
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Definition
Through any two points there is exactly one line.
Pg. 23 |
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Term
Postulate 7
# of points in a plane |
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Definition
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.
Pg. 23 |
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Term
Postulate 8
Lines in a plane |
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Definition
If two points are in a plane, then the line that contains the points is in that plane.
Pg. 23 |
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Term
Postulate 9
Intersecting planes |
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Definition
If two planes interest, then their intersection is a line.
Pg. 23 |
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Term
Theorem 1-1
Intersecting lines |
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Definition
If two lines intersect, then they intersect in exactly one point.
Pg. 23 |
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Term
Theorem 1-2
Forming a plane |
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Definition
Through a line and a point not in a line there is exactly one plane.
Pg. 23 |
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Term
| Theorem 1-3 Intersecting lines and planes |
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Definition
If two lines intersect, then exactly one plane contains the lines.
Pg. 23 |
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Term
If-Then Statements
Conditional Statements or conditionals |
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Definition
Example:
If B is bewtween A and C, then AB + AC =AC
or
If p, then q
Pg. 33 |
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Term
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Definition
The if part of an if-then statement
Pg. 33 |
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Term
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Definition
The then part of an if-then statement
Pg. 33 |
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Term
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Definition
When the hypothesis and conclusion are interchanged
Pg. 33 |
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Term
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Definition
When an example can be found where the hypothesis is true and the conclusion is false.
Pg. 33 |
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Term
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Definition
When a conditional and is converse are both true they can be combined into a single statement.
A statement that contains the words "if and only if"
Pg. 34 |
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Term
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Definition
If a = b and c = d, then a + c = b +d
This can also be used to add a number to both sides.
Example: a + 2 = b + 2
Pg. 37 |
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Term
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Definition
If a = b and c =d, then a - c = b + d
This can also be used to subtract a number from both sides
Example: a - 2 = b - 2
Pg. 37 |
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Term
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Definition
If a = b and c = d, then a -c = b -d
This can also be used to multiply both sides of the equation by the same number.
Example: 1/2a = 1/2b
Pg. 37 |
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Term
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Definition
If a = b and c ≠ 0, then a/c = b/c
Pg. 37 |
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Term
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Definition
If a =b, then either a or b may be substituted for the other in any equation (or inequality)
Pg. 37 |
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Term
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Definition
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Term
|
Definition
If a = b, then b = a
or
If < D ≅ < E, then < E ≅ < D
Pg. 37 |
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Term
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Definition
If a = b and b = c, then a =c
or
If < D ≅ < E and < E ≅ < F, the < D ≅ < F
Pg. 37 |
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Term
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Definition
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Term
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Definition
If M is the midpoint of seg AB, then AM = 1/2AB and MB = 1/2AB
Pg. 43 |
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Term
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Definition
If Ray BX is the bisector of < ABC, then
m< ABX = 1/2m< ABC and m< XBC = 1/2m< ABC
Pg. 44 |
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Term
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Definition
Given Information
Definitions
Postulates
Properties of Equality or Congruency
Theorems (that have already been proved)
Pg. 45 |
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Term
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Definition
Two angles whose measures have the sum of 90
Each angle is called a complement of the other.
Pg. 50 |
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Term
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Definition
Two angles whose measures have the sum of 180.
Each angle is called asupplement of the other.
Pg. 50 |
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Term
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Definition
Two angles that have sides consisting of opposite rays. When two lines interest, they form two pairs of vertical angles.
Pg. 51 |
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Term
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Definition
Vertical angles are Congruent
Pg. 51 |
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Term
Theorem 2-4
If two lines are ┴, then ___________ |
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Definition
If two lines are perpendicular, then they form congruent adjacent angles.
Pg. 56 |
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Term
Theorem 2-5
If two lines form ≅ adj. <'s, then ________ |
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Definition
If two lines form congruent adjacent angles, then the lines are perpendicular.
Pg. 56 |
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Term
Theroem 2-6
If the ext. sides of two adj. actue <'s are ┴, then ________ |
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Definition
If the exterior sides of two adjacent acute angles are perpendicular, then the angls are complementary.
Pg. 56 |
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Term
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Definition
Two lines that intersect to form right angles.
Pg. 56 |
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Term
Theorem 2-7
Supplements of ≅ <'s |
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Definition
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.
Pg. 61 |
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Term
Theorem 2-8
Complements of ≅ <'s |
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Definition
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.
Pg. 61 |
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