Geometry Proofs & Reasoning 3 — Questions and Answers
Question 1: What is the contrapositive of 'If a shape is a triangle, then it has three sides'?
- If a shape does not have three sides, then it is not a triangle (Correct answer)
- If a shape has three sides, then it is a triangle
- If a shape is not a triangle, then it does not have three sides
- A triangle always has three sides
Correct answer: If a shape does not have three sides, then it is not a triangle
The contrapositive negates and swaps both parts, and is logically equivalent to the original.
Question 2: In a two-column proof, the left column contains statements and the right column contains:
- Reasons or justifications (Correct answer)
- Diagrams
- Conclusions only
- Given information only
Correct answer: Reasons or justifications
Each statement in a two-column proof must be justified by a reason on the right.
Question 3: Which pairs of angles are always congruent when two lines intersect?
- Vertical angles (Correct answer)
- Adjacent angles
- Complementary angles
- Linear pair angles
Correct answer: Vertical angles
Vertical angles formed by intersecting lines are always congruent.
Question 4: The statement 'a = a' is an example of which property of equality?
- Reflexive property (Correct answer)
- Symmetric property
- Transitive property
- Substitution property
Correct answer: Reflexive property
The reflexive property of equality states that any quantity equals itself.
Question 5: If two angles form a linear pair, their measures add up to:
- 180 degrees (Correct answer)
- 90 degrees
- 360 degrees
- 45 degrees
Correct answer: 180 degrees
Angles in a linear pair are supplementary, summing to 180 degrees.
Question 6: Which statement is accepted as true without proof and used as a starting point?
- Postulate (Correct answer)
- Theorem
- Corollary
- Conclusion
Correct answer: Postulate
A postulate (or axiom) is a basic assumption accepted without proof.
Question 7: The symmetric property of equality states that if a = b, then:
- b = a (Correct answer)
- a = a
- a + b = 0
- a = c
Correct answer: b = a
The symmetric property allows an equality to be reversed.
Geometry Proofs & Reasoning 3
What is the contrapositive of 'If a shape is a triangle, then it has three sides'?