Download Practice

Name
Class
2-5
Date
Practice
Form G
Reasoning in Algebra and Geometry
Fill in the reason that justifies each step.
1. 0.25x 1 2x 1 12 5 39
Given
Combine like terms, using the
a. 9 Distributive Property.
2.25x 1 12 5 39
2.25x 5 27
b. 9 Subtraction Property of Equality
225x 5 2700
c. 9 Multiplication Property of Equality
d. 9 Division Property of Equality
x 5 12
2. Given: m/ABC 5 80
m/ABD 1 m/DBC 5 m/ABC
Angle Addition Postulate
(3x 1 3) 1 (6x 1 5) 5 80
Substitution Property
A
Combine like terms, using the Associative and Distributive Properties.
9x 1 8 5 80
a. 9
Subtraction Property of Equality
B
9x 5 72
b. 9
Division Property of Equality
x58
c. 9
3. Given: KL 5 3(PM)
5x 5 3(2x 2 4)
(3x 3)
(6x 5)
C
5x
K
Substitution Property
Distributive Property
a. 9
Subtraction Property of Equality
2x 5 212
b. 9
Multiplication Property of Equality
x 5 12
c. 9
L
2x 4
5x 5 6x 2 12
P
M
4. Given: XY 5 YZ
6m 17
8m 5
X
Y
8m 1 5 5 6m 1 17
Substitution Property
2m 1 5 5 17
a. 9 Subtraction Property of Equality
2m 5 12
b. 9 Subtraction Property of Equality
c. 9 Division Property of Equality
m56
D
Name the property of equality or congruence that justifies going from the first
statement to the second statement.
5. XY > TZ
6. 3(x 1 2) 5 15
TZ > XY
3x 1 6 5 15
Symmetric Property of Congruence
Distributive Property
8. /A > /B and /B > /C
7. 4n 1 6 2 2n 5 9
/A > /C
2n 1 6 5 9
Combine like terms, using the
Associative and Distributive Properties.
Transitive Property of
Congruence
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
43
Z
Name
Class
2-5
Date
Practice (continued)
Form G
Reasoning in Algebra and Geometry
9. Write a two-column proof.
Given: /QWT and /TWX are complementary.
Q
Prove: x 5 28
T
(2x)
Statements
Reasons
(x 6)
1) /QWT and /TWX are
1) 9 Given
X
W
complementary
2) m/QWT 1 m/TWX 5 90 2) 9 Definition of complementary angles
3) 2x 1 x 1 6 5 90
3) 9 Substitution Property
4) 3x 1 6 5 90
4) 9 Combine like terms.
5) 3x 5 84
5) 9 Subtraction Property of Equality
6) x 5 28
6) 9 Division Property of Equality
10. Developing Proof Fill in the missing statements or reasons
6x 5
for the two-column proof.
D
8x 1
E
F
Given: E is the midpoint of DF .
Prove: DE 5 23
Statements
Reasons
1) E is the midpoint of DF .
1) 9 Given
2) 9 DE 5 EF
2) Definition of midpoint
3) 6x 1 5 5 8x 2 1
3) 9 Substitution Property
4) 5 5 2x 2 1
4) 9 Subtraction Property of Equality
5) Addition Property of Equality
5) 9 6 5 2x
6) 9 3 5 x
7) DE 5 6x 1 5
6) Division Property of Equality
8) DE 5 6(3) 1 5
9) DE 5 23
8) 9 Substitution Property
7) Given
9) 9 Simplify.
11. Write a two-column proof.
A
Given: m/PMN 5 m/RBC
M
R
Prove: m/ABR 1 m/PMN 5 m/ABC
B
Reasons
Statements
P
C
1) mlPMN 5 mlRBC
1) Given
2) mlABR 1 mlRBC 5 mlABC
2) Angle Addition Postulate
3) mlABR 1 mlPMN 5 mlABC
3) Substitution Property
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
44
N