Conditionals
What’s the “if” part called?
Hypothesis
Pattern-based reasoning
Inductive
T/F: The Law of Detachment uses facts.
True
2-column proof has statements and
Reasons
A logical statement that has two parts, a hypothesis p and a conclusion q.
Conditional Statement
What’s the “then” part called?
Conclusion
Fact-based reasoning (used to write geometric proofs)
Deductive
The Law of Syllogism uses these letters
a=a
Reflexive
If two angles are complementary, then what is the sum of their measures?
90 degrees
If a quadrilateral has four right angles, then it is a rectangle. What is the hypothesis?
A quadrilateral has four right angles
2, 4, 8, 16 → next term? (Name the reasoning)
32
Inductive
If it rains, then it will be wet. It is raining today.
It is wet.
If AB=CD then CD=AB
Symmetric Property
Two lines that intersect and form a right angle
Perpendicular Lines
If a quadrilateral has four right angles, then it is a rectangle. What is the converse?
If a quadrilateral is a rectangle, then it has four right angles.
T/F: The sum of all even numbers is a positive number. If false, provide a counterexample.
False
-2+2=0, which is not a positive number
If square → rectangle and rectangle → 4 right angles, then square → ?
4 Right Angles
If x = y, then x + 8 = y + 8.
Addition Property of Equality
∠A ≅ ∠B → m∠A = m∠B
Definition of Conguent Angles
If a quadrilateral has four right angles, then it is a rectangle. What is the inverse?
If a quadrilateral does not have four right angles, then it is not a rectangle.
Inductive or Deductive? “It rained 3 days, so it rains every day.”
Inductive Reasoning
Illustrate the Law of Syllogism using letters
If p->q and q->r, then p->r.
If a=b & b=c, then a=c.
Transitive Property
The opposite of the original statement (uses ~)
Negation