Logic and Proof Flashcards

Questions and Answers

What is a conditional statement?

If q, then p.

If not q, then not p.

If p, then q. (correct)

If not p, then not q.

What is the inverse of a conditional statement?

If not p, then not q.

What is the converse of a conditional statement?

If q, then p.

What is the contrapositive of a conditional statement?

If not q, then not p. Signup and view all the answers

What does a bi-conditional statement signify?

p if and only if q. Signup and view all the answers

What does the Addition Property of Equality state?

If a = b, then a + c = b + c. Signup and view all the answers

What does the Subtraction Property of Equality state?

If a = b, then a - c = b - c. Signup and view all the answers

What does the Multiplication Property of Equality state?

If a = b, then ac = bc. Signup and view all the answers

What does the Division Property of Equality state?

If a = b, then a/c = b/c. Signup and view all the answers

What is the Distributive Property?

If a(b + c), then ab + ac. Signup and view all the answers

What does the Substitution Property state?

If a = b, then a may be substituted for b in any expression or equation. Signup and view all the answers

What does the Reflexive Property state?

For any real number, a = a. Signup and view all the answers

What does the Symmetric Property state?

If a = b, then b = a. Signup and view all the answers

What does the Transitive Property state?

If a = b and b = c, then a = c. Signup and view all the answers

What does the Reflexive Property of Congruence state?

A segment or angle is congruent to itself. Signup and view all the answers

What does the Symmetric Property of Congruence state?

If figure A is congruent to figure B, then figure B is congruent to figure A. Signup and view all the answers

What does the Transitive Property of Congruence state?

If figure A is congruent to figure B and figure B is congruent to figure C, then figure A is congruent to figure C. Signup and view all the answers

What is the Definition of Congruence for segments?

Two segments are congruent if they have equal lengths. Signup and view all the answers

What is the Definition of Congruence for angles?

⦟A ≅ ⦟B if and only if m⦟A = m⦟B. Signup and view all the answers

What is the Definition of Midpoint?

A point that divides a segment into two equal lengths. Signup and view all the answers

What is the Segment Addition Postulate?

If point B is on segment AC, then AB + BC = AC. Signup and view all the answers

What is the Definition of Angle Bisector?

A ray that divides an angle into two equal angles. Signup and view all the answers

What is the Definition of Complementary Angles?

Two angles that add up to 90 degrees. Signup and view all the answers

What is the Definition of Supplementary Angles?

Two angles that add up to 180 degrees. Signup and view all the answers

What is the Definition of Perpendicular?

Two lines that intersect at a 90 degree angle. Signup and view all the answers

What is the Definition of a Right Angle?

An angle whose measure is 90 degrees. Signup and view all the answers

What is the Angle Addition Postulate?

If point B is in the interior of angle A, then m⦟A = m⦟AB + m⦟BC. Signup and view all the answers

What does the Vertical Angles Theorem state?

If two angles are vertical, then they are congruent. Signup and view all the answers

What does the Complement Theorem state?

If two angles form a right angle, then they are complementary. Signup and view all the answers

What does the Supplement Theorem state?

If two angles form a linear pair, then they are supplementary. Signup and view all the answers

What does the Congruent Complements Theorem state?

If two angles are complementary to the same angle, then they are congruent. Signup and view all the answers

What does the Congruent Supplements Theorem state?

If two angles are supplementary to the same angle, then they are congruent. Signup and view all the answers

Study Notes

Logic Definitions

Conditional Statement: Formulated as "If p, then q", indicating a relationship between two propositions.
Inverse: Expressed as "If not p, then not q", denying both the hypothesis and conclusion of a conditional statement.
Converse: Stated as "If q, then p", flipping the hypothesis and conclusion of the original conditional.
Contrapositive: Formulated as "If not q, then not p", which shows the relationship between the negation of the conclusion and the negation of the hypothesis.
Bi-conditional: Defined as "p if and only if q", asserting that both conditions are equivalent.

Properties of Equality

Addition Property of Equality: States that if a = b, then adding the same number c to both sides keeps the equality true.
Subtraction Property of Equality: Indicates that if a = b, subtracting c from both sides maintains the equality.
Multiplication Property of Equality: If a = b, then multiplying both sides by the same non-zero number c retains equality.
Division Property of Equality: If a = b, dividing both sides by the same non-zero number c preserves the equality.
Distributive Property: Expresses that a(b + c) equals ab + ac, distributing a over the sum inside the parentheses.

Properties of Congruence

Substitution Property: States that if a = b, then a can replace b in any expression or equation without changing its truth value.
Reflexive Property: For any real number a, it is always true that a = a.
Symmetric Property: If a = b, then it also follows that b = a, highlighting mutual equality.
Transitive Property: If a equals b and b equals c, then a must equal c, establishing a chain of equality.

Congruence Definitions

Reflexive Property of Congruence: Every geometric figure is congruent to itself.
Symmetric Property of Congruence: If shape A is congruent to shape B, then shape B is congruent to shape A.
Transitive Property of Congruence: If shape A is congruent to shape B, and shape B to shape C, then shape A is congruent to shape C.

Congruence of Segments and Angles

Definition of Congruence (segments): Determines that two segments are congruent if they have the same length.
Definition of Congruence (angles): If ∠A ≅ ∠B, then m∠A = m∠B, signifying angles are congruent if their measures are equal.

Geometry Terminology

Definition of Midpoint: A point that divides a segment into two equal parts.
Segment Addition Postulate: States that if point B is between points A and C, then AB + BC = AC, where segment lengths are additive.
Definition of Angle Bisector: A ray that divides an angle into two congruent angles.
Definition of Complementary Angles: Two angles that sum up to 90 degrees.
Definition of Supplementary Angles: Two angles that sum up to 180 degrees.
Definition of Perpendicular: Two lines that meet at a right angle (90 degrees).
Definition of a Right Angle: An angle that measures precisely 90 degrees.

Angle Relationships

Angle Addition Postulate: If point D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC.
Vertical Angles Theorem: States that if two angles are vertical opposite each other, they are congruent.
Complement Theorem: If two angles form a right angle, they are complementary.
Supplement Theorem: If two angles form a linear pair, they are supplementary.

Theorems on Congruent Angles

Congruent Complements Theorem: States if two angles are complementary to the same angle, they are congruent.
Congruent Supplements Theorem: If two angles are supplementary to the same angle, they are congruent.

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Explore key concepts in logic and proof with these flashcards from Unit 2. Each card provides definitions for essential terms such as conditional statements, inverses, and contrapositive. Perfect for students looking to reinforce their understanding of logical reasoning.

Logic and Proof Flashcards - Unit 2