Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Algebra Fill in the reason that justifies each step.

5. 1 2 x − 5 = 10 1 half , x , minus , 5 equals , 10	Given
   2 ( 1 2 x − 5 ) = 20 2 . open . 1 half , x minus 5 . close . equals 20	a. ? ¯ modified question mark with under bar below
   x − 10 = 20 x minus , 10 equals , 20	b. ? ¯ modified question mark with under bar below
   x = 30 x equals , 30	c. ? ¯ modified question mark with under bar below

6. 5 ( x + 3 ) = − 4 5 open x plus , 3 close , equals negative 4	Given
   5 x + 15 = − 4 5 x plus . 15 equals negative 4	a. ? ¯ modified question mark with under bar below
   5 x = − 19 5 x equals negative 19	b. ? ¯ modified question mark with under bar below
   x = − 19 5 x equals negative , 19 over 5	c. ? ¯ modified question mark with under bar below

7. 

   ∠ C D E angle c d e  and ∠ E D F angle e d f  are supplementary.	that form a linear pair are supplementary
   m ∠ C D E + m ∠ E D F = 180 m angle c d e plus m angle e d f equals 180	a. ? ¯ modified question mark with under bar below
   x + ( 3 x + 20 ) = 180 x plus . open 3 x plus . 20 close equals 180	b. ? ¯ modified question mark with under bar below
   4 x + 20 = 180 4 x plus . 20 equals , 180	c. ? ¯ modified question mark with under bar below
   4 x = 160 4 x equals , 160	d. ? ¯ modified question mark with under bar below
   x = 40 x equals , 40	e. ? ¯ modified question mark with under bar below

8. X Y = 42 x y equals 42	Given
   X Z + Z Y = X Y x z plus z y equals x y	a. ? ¯ modified question mark with under bar below
   3 ( n + 4 ) + 3 n = 42 3 open n plus , 4 close plus , 3 n equals , 42	b. ? ¯ modified question mark with under bar below
   3 n + 12 + 3 n = 42 3 n plus . 12 plus . 3 n equals , 42	c. ? ¯ modified question mark with under bar below
   6 n + 12 = 42 6 n plus . 12 equals , 42	d. ? ¯ modified question mark with under bar below
   6 n = 30 6 n equals , 30	e. ? ¯ modified question mark with under bar below
   n = 5 n equals , 5	f. ? ¯ modified question mark with under bar below

   

See Problem 2.

Name the property of equality or congruence that justifies going from the first statement to the second statement.

9. 2 x + 1 = 7 2 x = 6 table with 2 rows and 1 column , row1 column 1 , 2 x plus . 1 equals , 7 , row2 column 1 , 2 x equals , 6 , end table
10. 5 x = 20 x = 4 table with 2 rows and 2 columns , row1 column 1 , 5 x equals , column 2 20 , row2 column 1 , x equals , column 2 4 , end table
11. S T ¯ ≅ Q R ¯ Q R ¯ ≅ S T ¯ table with 2 rows and 1 column , row1 column 1 , s t bar , approximately equal to , q r bar , row2 column 1 , q r bar , approximately equal to , s t bar , end table
12. A B − B C = 12 A B = 12 + B C table with 2 rows and 1 column , row1 column 1 , eh b minus b c equals 12 , row2 column 1 , eh b equals , 12 plus b c , end table

See Problem 3.

13. Developing Proof Fill in the missing statements or reasons for the following two-column proof.

    Given: C is the midpoint of A D ¯ . eh d bar , .

    Prove: x = 6 x equals , 6

    

    Statements	Reasons
    1) C is the midpoint of A D ¯ . eh d bar , .	1) a. ? ¯ modified question mark with under bar below
    2) A C ¯ ≅ C D ¯ eh c bar , approximately equal to , c d bar	2) b. ? ¯ modified question mark with under bar below
    3) A C = C D eh c , equals , c d	3) ≅ approximately equal to  segments have equal length.
    4) 4 x = 2 x + 12 4 x equals . 2 x plus , 12	4) c. ? ¯ modified question mark with under bar below
    5) d. ? ¯ modified question mark with under bar below	5) Subtraction Property of Equality
    6) x = 6 x equals , 6	6) e. ? ¯ modified question mark with under bar below

Table of Contents