Deductive Reasoning 3
Properties
Worksheet
Name _________________________
Due Date ____________ Period _____
For 1 – 22, name the property that justifies each statement.
1.
If y = 75 and y = mA, then mA = 75.
2.
If XY + AB = WZ + AB, then XY = WZ.
3.
If m1 + m2 =90 and m2 = m3, then m1 +m3 = 90.
4.
If 2mABC =180, then mABC = 90.
5.
If m1 + 30 = 90, then m1 = 60.
6.
If 3x = 15 and 5y = 15, then 3x =5y.
7.
If AB  CD , and CD  EF , then AB  EF .
8.
If RS = WT, then RS + ST = WT + ST.
9.
If 2x + 8 = 20, then 2x = 12.
10.
If 3x - 4 = 20, then 3x = 24.
11.
ZZ
12.
If 12x = 84, then x = 7.
13.
AB = AB
14.
If 3x + 14 = 80, then 3x = 66.
15.
2x + y = 5 and x = y, then 2x + x = 5.
16.
If AB – BC = 12, then AB = 12 + BC.
17.
If mA = 15, then 3mA = 45.
18.
If1  2 and 2  3, then 1   3.
19.
2(3x +5) = 10, then 6x + 10 = 10.
20.
If 3x + 5 = 50, then 3x = 45.
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Deductive Reasoning 3
21.
If MN = OP, then MN + HY = OP + HY.
22.
If A + B = C and A = 30, then 30 + B = C.
For 23 and 24, solve the algebra problem and give a reason for each step.
23.
2x + 20 = 30
24.
1
(8x – 6) = 37
2
For 25 through 29, classify each of the following as inductive or deductive reasoning.
25. A manufacturer tested two detergents, Brand A and Brand B on 7000 users. More than ¾
preferred Brand B. The manufacturer concluded that Brand B should be marketed and
Brand A should not.
26.
By measuring six linear pairs, Mabel concluded that two angles forming a linear pair are
supplementary.
27. From the definition of a right angle and of complementary angles, Sadie concludes that
the sum of the measures of two complementary angles is the measure of a right angle.
28. Sam attends a new school. His first Friday at school he had a math test. His second
Friday at school he had a math test. Sam concluded that every Friday he will have a
math test.
29. Fred was asked to solve the following algebra problem 2x = 10. He concluded x = 5.
30. What is the range of the function shown in the graph?
A
B
C
D
all real numbers
−1  x  3
−1  y  2
−2  y  1
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Deductive Reasoning 3
Deductive 3 Worksheet Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Substitution
Subtraction Property of Equality (SPOE)
Substitution
Division Property of Equality (DPOE)
Subtraction Property of Equality (SPOE)
Substitution
Transitive Property of Congruence
Addition Property of Equality (APOE)
Subtraction Property of Equality (SPOE)
Addition Property of Equality (APOE)
Reflexive Property
Division Property of Equality (DPOE)
Reflexive Property
Subtraction Property of Equality (SPOE)
Substitution
Addition Property of Equality (APOE)
Multiplication Property of Equality (MPOE)
Transitive Property of Congruence
Distributive Property
Subtraction Property of Equality (SPOE)
Addition Property of Equality (APOE)
Substitution
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Deductive Reasoning 3
23.
2x + 20 = 30
2x = 10
x=5
Given
Subtraction Property of Equality
Division Property of Equality
24.
½ (8x – 6) = 37
4x – 3 = 37
4x = 40
x = 10
Given
Distributive Property
Addition Property of Equality
Division Property of Equality
25.
26.
27.
28.
29.
30.
Inductive
Inductive
Deductive
Inductive
Deductive
D
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