Download Math Year 2

HW Unit 2 Review
Name: _____________________________
Period: ________ Date: ______________
Inductive Reasoning vs. Deductive Reasoning: For problem #1, state whether the thinking
process is deductive or inductive.
1. A math student draws 4 different triangles and measure each of the three angles contained in
the triangles. When she adds up the angle measures in each triangle she gets a sum of 180
degrees. The student concludes that the sum of the angle measures in every triangle is 180
degrees. ___Inductive Reasoning___________
2. A scientist observes that 5 of her 15 cactus plants grew in the month of July and the
remaining cacti did not. She concludes, using inductive reasoning, that the month of July is the
growing season for her particular type of cacti. Is this a fair conclusion? Explain.
___No. Since more didn’t grow than grew, it isn’t fair to say it is a good growing season. ___
3. Which is the best example of inductive reasoning?
___d______
A. A student measures the angles of one rectangle and finds they are all 90 degrees. The
student concludes the angles in every rectangle are 90 degrees.
B. A scientist observes on Monday that it takes a certain material 2 hours to decompose.
On Tuesday, the scientist observes the same material takes 3 hours to decompose, and
on Wednesday it takes 2 hours to decompose. The scientist concludes that it will
always take 2 hours for that type of material to decompose.
C. A math student observes that the number 126 is divisible by the number 6. The
student concludes that any number ending in 6 is divisible by 6.
D. A scientist observes during many tests that a certain bacteria colony doubles in size
within an hour. The scientist concludes that this bacteria colony will always double
in size within an hour.
Explain you reasoning for #3. ___There were many tests ran, every time the colony doubles in
size within an hour, and the conclusion states what she saw. _________________________
Complete the following patterns. Then write a rule for each pattern.
4. 1, 2, 6, 24, 120,720
Rule: ___Multiply by the next consecutive integers
5. …, H, I, L, M, P, Q, T, U
Rule: ___Write 2 letters, skip 2 letters
6. 84, 42, 14, 7 , 7 , 7/60, 1/60
2 10
Rule: ___Divide by the next consecutive integer
7. 9, 27, 108, 540, 3240, 22680
Rule: ___Multiply by the next consecutive integers
Using Deductive Reasoning: Use deductive thinking to write a conclusion.
8. All whole numbers are rational numbers. 4 is a whole number.
Your conclusion: __4 is a rational number. _____
9. The sum of any two odd numbers is even. A and B are not both odd numbers.
Your conclusion: ___None_____
10. The difference of any two even numbers is even. A and B are both even numbers.
Your conclusion: The difference between A and B is even. _____
Conditional, Converse, Inverse, Contrapositive: Complete the table.
11. All squares are parallelograms.
Conditional
If a quadrilateral is a square then it is a parallelogram.
T or F
Converse
If a quadrilateral is a parallelogram then it is a square.
T or F
rectangle
If a quadrilateral is not a square then it is not a parallelogram.
Inverse
T or F
rectangle
Contrapositive If a quadrilateral is not a parallelogram then it is not a square.
T or F
12. Right angles have a measure of 90 degrees.
Conditional
If an angle is a right angle, then it has a measure of 90 degrees.
T or F
Converse
If an angle has a measure of 90 degrees then it is a right angle.
T or F
Inverse
If an angle is not a right angle, then it does not have a measure of 900.
T or F
Contrapositive If an angle doesn’t have a measure of 90 degrees then it isn’t a right angle.
T or F
Logical Order: Arrange the statements in logical order.
13. A, D,C,B,E
A.
B.
C.
D.
E.
If Hamilton’s football team practices well, then they will be a great team.
If there are many pep assemblies, then we will miss class time.
If Hamilton’s football team goes to state, then there will be many pep assemblies.
If Hamilton’s football team is great, then they will go to state.
If we miss class time, then our test date will be delayed.
Pre-Proofs: Give your conclusion and reason.
14. Given:
X
Z
Y
Conclusion: XY + YZ = XZ
Reason: Segment addition Property
1
15. Given:
2
Conclusion: <1 and <2 form a linear pair
Reason: Definition of linear pair.
Proof: Complete the following proofs.
16. Given: C is the midpoint of AB .
Prove: the value of x
7x - 5
A
5x + 1
C
B
Statements
Reasons
1. C is the midpoint of AB .
1. Given
2. AC = CB
3. 7x-5 = 5x+1
4. 2x – 5 = 1
5. 2x = 6
6. x = 3
2. Definition of midpoint
3. Substitution Property of Equality
4. Subtraction property of Equality
5. Addition Property of Equality
6. Division Property of Equality
B
17. Given: AD ; AD = AB
Prove: AK + KD = AB
D
K
A
Statements
Reasons
1. AD
1.
Given
2. AK + KD = AD
2.
Segment addition Property
3. AD = AB
3.
Given
4. AK + KD = AB
4.
Substitution
18. Given: RO  NY
Prove: RN = OY

R

N
O
Statements
Reasons
1. RO  NY
1.
2. RO = NY
2. Def. of congruence
3. ON = ON
3.
4. RO + ON = ON + NY
4.
5. RO + ON = RN
5. Segment Addition
6. ON + NY = OY
6.
Segment Additon
7.
7.
Substitution
RN = OY
Y
Given
Reflexive Property of Equality
Addition Property of Equality
Angle Pair Names: Refer to the figure. Give the name of each pair of angles and state their
relationship (congruent, some of 180, or no conclusion).
19. 3 and 5 Alternate Interior Angles, Congruent
7
8
20. 1 and 7 Alternate Exterior Angles, Congruent
21. 2 and 4 Vertical Angles, Congruent
5
6
3
4
1
2
22. If m2 = 5x + 12 and m6 = 7x - 10, then m2 = 67
23. If m4 = 5x + 8 and m5 = 14x + 1, then m8 = 53
Proving Parallel Lines: Using the given information, which lines, if any, can you conclude
parallel? Justify each conclusion with a theorem or postulate.
24. 2  8 Alternate Exterior Angles Congruent(Converse of Parallel Lines Theorem)
7
8
25. 2  7 None
5
l
6
26. m3 + m6 = 180 Add to 180 (Same Side Interior Angles - Supplementary
4 3
1
2
27. 4  6 Alternate Interior Angles Congruent (Converse of Parallel Lines Theorem)
m