Unit 2: Reasoning and Proofs Flashcards
The Symbol for a Conditional Statement:
p → q
Symbol for a Negation:
~p
Symbol for a Converse:
q → p
Symbol for an Inverse:
~p → ~q
Symbol for a Contrapositive:
~q → ~p
Symbol for a Biconditional Statement:
p ↔ q (if and only if)
A __________ is an unproven statement that is based on observations.
Conjecture
You use _________ _________ when you find a pattern in specific cases and then write a conjecture for the general case.
Inductive Reasoning
___________ ________ are those numbers that follow each other. They follow in a sequence or in order.
Consecutive Integers
An example that disproves a statement (shows that it is false).
Counterexample
_________ _________ uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.
Deductive Reasoning
If the hypothesis of a true conditional statement is true, then the conclusion is also true.
Law of Detachment
If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
If hypothesis p, then conclusion r.
Law of Syllogism
Name the postulate: Through any two points, there exists exactly one line.
Two Point Postulate
Name the postulate: A line contains at least two points.
Line-Point Postulate
Name the postulate: If two lines intersect, then their intersection is exactly one point.
Line Intersection Postulate
Name the postulate: Through any three noncollinear points, there exists exactly one plane.
Three Point Postulate
Name the postulate: A plane contains at least three noncollinear points.
Plane-Point Postulate
Name the postulate: If two points lie in a plane, then the line containing them lies in the plane.
Plane-Line Postulate
Name the postulate: If two planes intersect, then their intersection is a line.
Plane Intersection Postulate
If a = b, then a + c = b + c
Additional Property of Equality
If a = b, then a - c = b - c
Subtraction Property of Equality
If a = b, then a × c = b × c, c ≠ 0
Multiplication Property of Equality
If a =b, then a/c = b/c, c ≠ 0
Division Property of Equality
If a = b, then a can be substituted for b (or b for a) in any equation or expression.
Substitution Property of Equality
a = a
Reflective Property of Equality
If a = b, then b = a
Symmetric Property of Equality
If a = b and b = c, then a = c
Transitive Property of Equality
For any segment AB, Segment AB ≅ Segment AB
Reflexive Property of Congruence
If Segment AB ≅ Segment CD, then Segment CD ≅ Segment AB
Symmetric Property of Congruence
If Segment AB ≅ Segment CD and Segment CD ≅ Segment EF, then Segment AB ≅ EF
Transitive Property of Congruence
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
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
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
The measure of two angles are equal if and only if the angles are congruent.
m∠A = m∠B ↔ ∠A ≅ ∠B
Definition of Congruence
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
Two angles are complementary if and only if the sum of their measures is 90°.
Complementary ↔ Sum is 90°
Definition of Complementary Angles
Two angles are supplementary if and only if the sum of their measures is 180°.
Supplementary ↔ Sum is 180°
Definition of Supplementary Angles
An angle bisector divides an angle into two equal parts.
Definition of an Angle Bisector
Perpendicular lines form right angles.
Definition of Perpendicular
m∠ABD + m∠DBC = m∠ABC
(name the postulate)
Angle Addition Postulate
If two angles are vertical, then they are congruent.
Vertical → Congruent
Vertical Angles Theorem
If two angles form a right angle, then they are complementary.
Form a Right Angle → Complementary
Compliment Theorem
If two angles form a linear pair, then they are supplementary.
Form A Linear Pair → Supplementary
Linear Pair Theorem (Supplement Theorem)
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
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
