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- P Q P and Q
- T T T
- T F F
- F T F
- F F F
- P Q P or Q
- T T T
- T F T
- F T T
- F F F
Conditional Statement (implication)
- If P, then Q
- P (the hypothesis)
- Q (the conclusion)
- An inspiration leading to the statement of a theory.
- Intuition suggests....
An organized effort to test and validate the theory.
We use specific observations and experiments to draw a general conclusion.
A formal argument that proves the tested theory.
the type of reasoning in which the knowledge and acceptance of assumptions guarantee the truth of a particluar conclusion.
Valid argument (deductive reasoning)
LAW OF DETACHMENT
- If P, then Q (premises)
- P .
- therefore Q (conclusion)
A good definition possess what qualities?
- 1. It names the term being defined.
- 2. It places the term into a set or category.
- 3. It distinguishes the defined term from other terms without providing unnecessary facts.
- 4. It is reversible.
Considering the definition, "A line segment is the part of a line that consists of two points, known as endpoints, and all points between them" we see that the definition is good because it possesses:
- 1. the term being defined, line segment.
- 2. a line segment is defined as part of a line (category)
- 3. the definition distinguishes the line segment as a specific part of a line.
- 4. The definition is reversible "a line segment is the part of a line between and including two points." "The part of a line between and including two points is a line segment."
A postulate is
assumed to be true.
If X is a point on line segment AB and A-X-B, then AX + XB = AB
The Midpoint of a line segment is
the point that separates the line segment into two congruent parts.
GIVEN: M is the midpoint of line segment EF.
EM = 3x+ 9 and
MF = x + 17
FIND: x and EM
- Because M is the midpoint of line segment EF, EM = MF.
- Therefore, 3x + 9 = x + 17
- x = 4
are two rays with a common endpoint. The union of opposite rays is a straight line.
are lines that lie in the same plane but do not intersect.
A plane is what dimension.
A plan is two-dimensional; it has infinite length and infinite width but no thickness.
A plane has what three characteristics?
two-dimensional, consists of an infinite number of points, and contains an infinite number of lines.
Space has what three characteristics?
The set of all possible points. It is three-dimensional, having qualities of length, width, and depth.
If two planes or lines do not intersect they are....
The measure of an angle is a unique positive number.
An angle whose measure is less than 90 degrees is
an acute angle
An angle whose measure is between 90 and 180 degrees is an
An angle whose measure is exactly 180 degrees is a
An angle whose measure is between 180 and 360 degrees is
a reflex angle.
If a point D lies in the interior of an angle ABC, then the measure of angle ABD + the measure of angle DBC = the measure of angle ABC.
If two angles have a common vertex and a common side between them they are
If two angles have the same measure they are
The ray that separates the given angle into two congruent angles is the
bisector of an angle.
If the sum of two angles meausre 90 degrees. What are they and what are they known as?
The two angles are complementary and are known as the complement of the other angle.
If the sum of two angles measures 180 degrees. Each angle in the pair is known as ___________ and the two angles are ________________.
- supplement of the other angle.
When two straight lines intersect, the pairs of nonadjacent angles in opposite positions are known as
Addition Property of Equality (a, b, and c are real numbers)
If a = b, then a + c = b + c
Subtraction Property of Equality (a, b, and c are real numbers)
If a = b, then a - c = b - c
Multiplication Property of Equality (a, b, and c are real numbers)
If a = b, then a * c = b * c
Division Property of Equality (a, b, and c are real numbers)
If a = b and c
0, then a/c = b/c
Reflexive Property of Equality (a, b, and c are real numbers)
a = a
Symmetric Property of Equality (a, b, and c are real numbers)
If a = b, then b = a
Distributive Property of Equality (a, b, and c are real numbers)
a(b + c) = a * b + a * c
Substitution Property of Equality (a, b, and c are real numbers)
If a = b, then a replaces b in any equation.
Transitive Property of Equality (a, b, and c are real numbers)
If a = b and b = c, then a = c