Name
LESSON
2-5
Date
Class
Practice A
Algebraic Proof
For Exercises 1–12, write the letter of each property next to its definition.
The letters a, b, and c represent real numbers.
F
1. If a ⫽ b, then b ⫽ a.
C
2. If a ⫽ b, then ac ⫽ bc.
_
_
A. Addition Property of Equality
B. Subtraction Property of Equality
J
3. AB AB
C. Multiplication Property of Equality
E
4. a ⫽ a
D. Division Property of Equality
5. If a ⫽ b, then a ⫹ c ⫽ b ⫹ c.
A
E. Reflexive Property of Equality
I
6. a(b ⫹ c) ⫽ ab ⫹ ac
F. Symmetric Property of Equality
G
7. If a ⫽ b and b ⫽ c, then a ⫽ c.
G. Transitive Property of Equality
8. If ⬔P ⬔Q, then
⬔Q ⬔P.
K
H. Substitution Property of Equality
I. Distributive Property
9. If ⬔A ⬔B and ⬔B ⬔C,
then ⬔A ⬔C.
L
b.
a ⫽ __
D
10. If a ⫽ b and c ⫽ 0, then __
c
c
11. If a ⫽ b, then b can be substituted for a
in any expression.
H
12. If a ⫽ b, then a ⫺ c ⫽ b ⫺ c.
J. Reflexive Property of Congruence
K. Symmetric Property of
Congruence
L. Transitive Property of Congruence
B
13. Cali measures her textbook and finds that it is 8 inches wide. She wants to know
how many centimeters wide her textbook is. The formula to convert inches to
centimeters is 2.54i ⫽ c, where i is the length in inches and c is the length in
centimeters. Fill in the blanks to find the answer. The justifications will guide you.
2.54i ⫽ c
2.54(
Given equation
8 )⫽c
20.32 ⫽ c
c
⫽ 20.32
Substitution Property of Equality
Simplify.
Symmetric Property of Equality
14. Write a justification for each step.
11
$
1
–X
3
1 %
7
&
Seg. Add. Post.
DE ⫹ EF ⫽ DF
__31 x ⫹ 1 ⫹ 7 ⫽ 11
Subst.
Simplify.
1 x ⫹ 8 ⫽ 11
__
3
Subtr. Prop. of ⫽
1x ⫽ 3
__
3
Mult. Prop. of ⫽
x⫽9
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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