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If-Then Statements
Conditional Statements or conditionals |
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Definition
Example:
If B is bewtween A and C, then AB + AC =AC
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If p, then q
Pg. 33 |
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Definition
The if part of an if-then statement
Pg. 33 |
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Definition
The then part of an if-then statement
Pg. 33 |
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Definition
When the hypothesis and conclusion are interchanged
Pg. 33 |
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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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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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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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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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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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Definition
If a = b and c ≠ 0, then a/c = b/c
Pg. 37 |
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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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Definition
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Definition
If a = b, then b = a
or
If < D ≅ < E, then < E ≅ < D
Pg. 37 |
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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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Definition
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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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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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Definition
Given Information
Definitions
Postulates
Properties of Equality or Congruency
Theorems (that have already been proved)
Pg. 45 |
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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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Definition
Two angles whose measures have the sum of 180.
Each angle is called asupplement of the other.
Pg. 50 |
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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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Definition
Vertical angles are Congruent
Pg. 51 |
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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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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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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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Definition
Two lines that intersect to form right angles.
Pg. 56 |
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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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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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