Unit 2: Reasoning and Proofs Flashcards

1
Q

The Symbol for a Conditional Statement:

A

p → q

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2
Q

Symbol for a Negation:

A

~p

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3
Q

Symbol for a Converse:

A

q → p

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4
Q

Symbol for an Inverse:

A

~p → ~q

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5
Q

Symbol for a Contrapositive:

A

~q → ~p

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6
Q

Symbol for a Biconditional Statement:

A

p ↔ q (if and only if)

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7
Q

A __________ is an unproven statement that is based on observations.

A

Conjecture

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8
Q

You use _________ _________ when you find a pattern in specific cases and then write a conjecture for the general case.

A

Inductive Reasoning

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9
Q

___________ ________ are those numbers that follow each other. They follow in a sequence or in order.

A

Consecutive Integers

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10
Q

An example that disproves a statement (shows that it is false).

A

Counterexample

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11
Q

_________ _________ uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

A

Deductive Reasoning

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12
Q

If the hypothesis of a true conditional statement is true, then the conclusion is also true.

A

Law of Detachment

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13
Q

If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
If hypothesis p, then conclusion r.

A

Law of Syllogism

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14
Q

Name the postulate: Through any two points, there exists exactly one line.

A

Two Point Postulate

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15
Q

Name the postulate: A line contains at least two points.

A

Line-Point Postulate

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16
Q

Name the postulate: If two lines intersect, then their intersection is exactly one point.

A

Line Intersection Postulate

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17
Q

Name the postulate: Through any three noncollinear points, there exists exactly one plane.

A

Three Point Postulate

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18
Q

Name the postulate: A plane contains at least three noncollinear points.

A

Plane-Point Postulate

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19
Q

Name the postulate: If two points lie in a plane, then the line containing them lies in the plane.

A

Plane-Line Postulate

20
Q

Name the postulate: If two planes intersect, then their intersection is a line.

A

Plane Intersection Postulate

21
Q

If a = b, then a + c = b + c

A

Additional Property of Equality

22
Q

If a = b, then a - c = b - c

A

Subtraction Property of Equality

23
Q

If a = b, then a × c = b × c, c ≠ 0

A

Multiplication Property of Equality

24
Q

If a =b, then a/c = b/c, c ≠ 0

A

Division Property of Equality

25
If a = b, then a can be substituted for b (or b for a) in any equation or expression.
Substitution Property of Equality
26
a = a
Reflective Property of Equality
27
If a = b, then b = a
Symmetric Property of Equality
28
If a = b and b = c, then a = c
Transitive Property of Equality
29
For any segment AB, Segment AB ≅ Segment AB
Reflexive Property of Congruence
30
If Segment AB ≅ Segment CD, then Segment CD ≅ Segment AB
Symmetric Property of Congruence
31
If Segment AB ≅ Segment CD and Segment CD ≅ Segment EF, then Segment AB ≅ EF
Transitive Property of Congruence
32
Segments are congruent if and only if they have the same measure: If Segment AB ≅ Segment CD, then AB = CD If AB = CD, then Segment AB ≅ Segment CD
Definition of Congruence
33
The midpoint of a segment divides the segment into two congruent parts (equal lengths). If M is the midpoint of segment AB, then AM = MB
Definition of Midpoint
34
If A, B, and C are colinear points and B is between A and C, then AB + BC = AC (name the postulate)
Segment Addition Postulate
35
The measure of two angles are equal if and only if the angles are congruent. m∠A = m∠B ↔ ∠A ≅ ∠B
Definition of Congruence
36
An angle measures 90° if and only if it is a right angle. m∠A = 90° ↔ ∠A is a right angle
Definition of a Right Angle
37
Two angles are complementary if and only if the sum of their measures is 90°. Complementary ↔ Sum is 90°
Definition of Complementary Angles
38
Two angles are supplementary if and only if the sum of their measures is 180°. Supplementary ↔ Sum is 180°
Definition of Supplementary Angles
39
An angle bisector divides an angle into two equal parts.
Definition of an Angle Bisector
40
Perpendicular lines form right angles.
Definition of Perpendicular
41
m∠ABD + m∠DBC = m∠ABC (name the postulate)
Angle Addition Postulate
42
If two angles are vertical, then they are congruent. Vertical → Congruent
Vertical Angles Theorem
43
If two angles form a right angle, then they are complementary. Form a Right Angle → Complementary
Compliment Theorem
44
If two angles form a linear pair, then they are supplementary. Form A Linear Pair → Supplementary
Linear Pair Theorem (Supplement Theorem)
45
If two angles complementary to the same angle, then they are congruent. (If ∠A is complementary to ∠B and ∠C is complementary to ∠B, then ∠A ≅ ∠C)
Congruent Compliments Theorem
46
If two angles supplementary to the same angle, then they are congruent. (If ∠A is supplementary to ∠B and ∠C is supplementary to ∠B, then ∠A ≅ ∠C)
Congruent Supplements Theorem