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Geometry - Chapter 2
Tehachapi High School Geometry Book
28
Mathematics
10th Grade
11/29/2012

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Term
If-Then Statements
Conditional Statements or conditionals
Definition
Example:
If B is bewtween A and C, then AB + AC =AC
or
If p, then q
Pg. 33
Term
Hypothesis
Definition
The if part of an if-then statement
Pg. 33
Term
Conclusion
Definition
The then part of an if-then statement
Pg. 33
Term
Converse
Definition
When the hypothesis and conclusion are interchanged
Pg. 33
Term
Counterexample
Definition
When an example can be found where the hypothesis is true and the conclusion is false.
Pg. 33
Term
Biconditional
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
Term
Addition
Property
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
Term
Subtraction
Property
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
Term
Multiplication Property
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
Term
Division Property
Definition
If a = b and c ≠ 0, then a/c = b/c
Pg. 37
Term
Subsititution Property
Definition
If a =b, then either a or b may be substituted for the other in any equation (or inequality)
Pg. 37
Term
Reflexive Property
Definition
a =a
or
< D ≅ < D
Pg. 37
Term
Symmetric
Property
Definition
If a = b, then b = a
or
If < D ≅ < E, then < E ≅ < D
Pg. 37
Term
Transitive
Property
Definition
If a = b and b = c, then a =c
or
If < D ≅ < E and < E ≅ < F, the < D ≅ < F
Pg. 37
Term
Distributive
Property
Definition
a(d+c) = ad +ac
Pg. 38
Term
Midpoint Theorem
Definition
If M is the midpoint of seg AB, then AM = 1/2AB and MB = 1/2AB
Pg. 43
Term
Angle Bisector
Theorem
Definition
If Ray BX is the bisector of < ABC, then
m< ABX = 1/2m< ABC and m< XBC = 1/2m< ABC
Pg. 44
Term
Reasons Used in
Proofs
Definition
Given Information
Definitions
Postulates
Properties of Equality or Congruency
Theorems (that have already been proved)
Pg. 45
Term
Complentary
Angles
Definition
Two angles whose measures have the sum of 90
Each angle is called a complement of the other.
Pg. 50
Term
Supplementary
Angles
Definition
Two angles whose measures have the sum of 180.
Each angle is called asupplement of the other.
Pg. 50
Term
Vertical Angles
Definition
Two angles that have sides consisting of opposite rays. When two lines interest, they form two pairs of vertical angles.
Pg. 51
Term
Vertical Angle Theorem
Definition
Vertical angles are Congruent
Pg. 51
Term
Theorem 2-4
If two lines are ┴, then ___________
Definition
If two lines are perpendicular, then they form congruent adjacent angles.
Pg. 56
Term
Theorem 2-5
If two lines form ≅ adj. <'s, then ________
Definition
If two lines form congruent adjacent angles, then the lines are perpendicular.
Pg. 56
Term
Theroem 2-6
If the ext. sides of two adj. actue <'s are ┴, then ________
Definition
If the exterior sides of two adjacent acute angles are perpendicular, then the angls are complementary.
Pg. 56
Term
Perpendicular
Lines
Definition
Two lines that intersect to form right angles.
Pg. 56
Term
Theorem 2-7
Supplements of ≅ <'s
Definition
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.
Pg. 61
Term
Theorem 2-8
Complements of ≅ <'s
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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