Proof
Jeopardy
Conditionals
Algebraic
Proofs
Geometric
Proofs
Postulates
Properties
Theorems
Definitions
100
100
100
100
200
200
200
200
300
300
300
300
400
400
400
400
Question:
Another name for an “if-then” statement is…
Answer:
Conditional Statement
100
Question:
Everything after the word if is called the ____________, and
everything after the word then is called the _____________.
Answer:
Hypothesis; Conclusion
200
Question:
Turn the following statement into a conditional:
All CD’s are round.
Answer:
If it is a CD, then it is round.
300
Question:
1. What is the converse of the following statement:
If Susan wins Proofs Jeopardy, then she will make an A on my test.
2. Is the converse true or false?
3. If false, state a counterexample.
Answer:
1. If Susan makes an A on my test, then she won Proofs Jeopardy.
2. False
3. Susan makes an A, but did not win Jeopardy.
400
Question:
Name 5 properties that might be used as
reasons in an Algebraic Proof.
Answer:
Choose 5: Addition Property of Equality, Subtraction P.O.E.,
Multiplication P.O.E., Division P.O.E., Distributive P.O.E., Symmetric
P.O.E., Reflexive P.O.E., Substitution P.O.E., Transitive P.O.E.
100
Question:
What are the next statement and reason for the following proof:
Statements
𝑚+2
4=
6
Reasons
𝐺𝑖𝑣𝑒𝑛
Answer:
Statement: 24 = 𝑚 + 2 Reason: 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑜𝑓 𝐸𝑞𝑢𝑎𝑙𝑖𝑡𝑦
200
Question:
List all corrections needed for the following proof:
𝐼𝑓 21 = 7 𝑝 − 3 , 𝑡ℎ𝑒𝑛 𝑝 = 6.
Statements
Reasons
1. 21 = 7 𝑝 − 3
1. Given
2. 𝑝 = 6
2. Given
3. 21 = 7𝑝 − 21
3. Multiplication P.O.E.
4. 0 = 7𝑝
4. Addition P.O.E.
5. 𝑝 = 0
5. Division P.O.E.
Answer:
•
•
•
•
•
#2 statement and reason should be taken out
Reason #3 should be Distributive Property of Equality (written out)
Statement #4 should be 42 = 7𝑝
Statement #5 should be 6 = 𝑝
Add in #6 statement: 𝑝 = 6, and #6 reason: Symmetric P.O.E.
300
Question:
Write either a flowchart or 2-column proof for the following:
𝑤−6
𝐼𝑓 15 =
, 𝑡ℎ𝑒𝑛 𝑤 = 36.
2
Answer:
Statements
1.
Given
2. 30 = 𝑤 − 6
2.
Multiplication
Property of Equality
3. 36 = 𝑤
3. Addition P.O.E.
4. 𝑤 = 36
4. Symmetric P.O.E.
1. 15 =
15 =
𝑤−6
2
Given
𝑤−6
2
Reasons
30 = 𝑤 − 6
Multiplication
Property of Equality
36 = 𝑤
Addition P.O.E.
𝑤 = 36
Symmetric P.O.E.
400
Question:
Identify the next reason for the following proof
Statements
Reasons
1. 𝐴𝐵𝐶 ≅ 𝐷𝐸𝐹
1. Given
2. 𝑚𝐴𝐵𝐶 = 𝑚𝐷𝐸𝐹
2.
Answer:
Definition of Congruent Angles
100
Question:
Fill in the following 2-column proof
𝑮𝑯 = 𝟑𝑭𝑮
Given
𝑯𝑱 = 𝟐𝑭𝑮
Given
Reflexive Property of Equality
Segment Addition Postulate
𝑭𝑱 = 𝑭𝑮 + 𝟑𝑭𝑮 + 𝟐𝑭𝑮
𝑭𝑱 = 𝟔𝑭𝑮
Addition P.O.E.
Answers: See answers above.
200
Question:
Make corrections to the following proof.
Reasons
Statements
1. 2 𝑎𝑛𝑑3 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
1. Given
2. 𝑚2 + 𝑚3 = 90°
2. Complementary Angles Property
3. 1 = 3
3. Given
4.
1 =
3
4. Definition of Congruent Segments
5. 𝑚2 + 𝑚3 = 180°
5. Substitution Property of Congruence
6. 2 𝑎𝑛𝑑1 𝑎𝑟𝑒 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡
6. Definition of Congruent Angles
Answers: See answers above.
300
Question:
Write a 2-column or flowchart proof for the following
𝐼𝑓 𝑚𝑃𝑄𝑅 = 4𝑥 𝑎𝑛𝑑 𝑚𝑅𝑄𝑆 = 2𝑥, 𝑡ℎ𝑒𝑛 𝑚𝑃𝑄𝑆 = 6𝑥.
Answer:
Statements
Reasons
1. 𝑚𝑃𝑄𝑅 = 4𝑥
1. Given
2. 𝑚𝑅𝑄𝑆 = 2𝑥
2. Given
3. 𝑚PQR + 𝑚𝑅𝑄𝑆 = 𝑚𝑃𝑄𝑆 3. Angle Addition Postulate
4. 4𝑥 + 2𝑥 = 𝑚𝑃𝑄𝑆
4. Substitution Property of Equality
5. 6𝑥 = 𝑚𝑃𝑄𝑆
5. Addition P.O.E.
6. 𝑚𝑃𝑄𝑆 = 6𝑥
6. Symmetric P.O.E.
400
Question:
Identify the postulate, property, theorem, or definition that best fits
𝑒
𝐼𝑓 = 7, 𝑡ℎ𝑒𝑛 𝑒 = 21
3
Answer:
Multiplication Property of Equality
100
Question:
Identify the postulate, property, theorem, or definition that best fits
𝐼𝑓 𝑚𝑅𝐿𝑀 = 90°, 𝑎𝑛𝑑 90° = 𝑚3, 𝑡ℎ𝑒𝑛 𝑚𝑅𝐿𝑀 = 𝑚3.
Answer:
Transitive Property of Equality
200
Question:
Identify the reasons that best fit
Statements
Reasons
1. 1 𝑎𝑛𝑑2 𝑓𝑜𝑟𝑚 𝑎 𝑙𝑖𝑛𝑒𝑎𝑟 𝑝𝑎𝑖𝑟𝑠
1.
2. 1 𝑎𝑛𝑑2 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
2.
3. 𝑚1 + 𝑚2 = 180°
3.
Answer:
1. Given
2. Linear Pairs are Supplementary
3. Definition of Supplementary Angles
300
Question:
Given the following information, what postulate, property, theorem
and you most likely going to use.
𝐼𝑓 𝐺𝑀 = 10 𝑎𝑛𝑑 𝐺𝐶 = 27, 𝑡ℎ𝑒𝑛 𝑀𝐶 = 17.
Answer:
Segment Addition Postulate
400