Geometry Proofs & Reasoning 2 — Questions and Answers
Question 1: Which type of reasoning moves from specific observations to a general conclusion?
- Inductive reasoning (Correct answer)
- Deductive reasoning
- Circular reasoning
- Transitive reasoning
Correct answer: Inductive reasoning
Inductive reasoning forms a general conjecture based on specific observed patterns.
Question 2: A conditional statement has the form 'If p, then q.' What is p called?
- Hypothesis (Correct answer)
- Conclusion
- Converse
- Contrapositive
Correct answer: Hypothesis
In 'if p, then q,' p is the hypothesis and q is the conclusion.
Question 3: What is the converse of 'If it is a square, then it is a rectangle'?
- If it is a rectangle, then it is a square (Correct answer)
- If it is not a square, then it is not a rectangle
- If it is not a rectangle, then it is not a square
- A square is always a rectangle
Correct answer: If it is a rectangle, then it is a square
The converse swaps the hypothesis and conclusion of a conditional statement.
Question 4: Which property justifies the statement 'If AB = CD and CD = EF, then AB = EF'?
- Transitive property (Correct answer)
- Reflexive property
- Symmetric property
- Distributive property
Correct answer: Transitive property
The transitive property states that if a = b and b = c, then a = c.
Question 5: A statement that has been proven true and can be used to prove other statements is called a:
- Theorem (Correct answer)
- Postulate
- Conjecture
- Hypothesis
Correct answer: Theorem
A theorem is a statement that has been proven using logic and previous results.
Question 6: What is a single example that proves a conjecture false called?
- Counterexample (Correct answer)
- Corollary
- Lemma
- Axiom
Correct answer: Counterexample
A counterexample is one case where the conjecture fails, disproving it.
Question 7: The reflexive property of congruence states that a segment is congruent to:
- Itself (Correct answer)
- Any equal segment
- Its midpoint
- Its perpendicular bisector
Correct answer: Itself
The reflexive property says any figure or segment is congruent to itself.
Geometry Proofs & Reasoning 2
Which type of reasoning moves from specific observations to a general conclusion?