Parallel and Perpendicular Lines Worksheet

**Page 1**

1.

$\angle $A and $\angle $B are congruent and supplementary. Prove that $\angle $A and $\angle $B are right angles.

Given:

Prove:

Correct answer : (0)

2.

What conclusion follows from the following pair of statements?

1. If two non vertical lines are perpendicular, then the product of their slopes is - 1.

2. The product of the slopes of non vertical lines $l$ and $n$ is not - 1.

1. If two non vertical lines are perpendicular, then the product of their slopes is - 1.

2. The product of the slopes of non vertical lines $l$ and $n$ is not - 1.

a. | $l$ is not perpendicular to $n$ | ||

b. | $l$ || $n$ | ||

c. | $l$ $\perp $ $n$ |

As product of slopes of

Correct answer : (1)

3.

Given:

Prove:

Correct answer : (0)

4.

It is given that $m$$\angle $A = $m$$\angle $B . Which of the following is the reason for the statement: $\angle $A $\cong $ $\angle $B?

a. | transitive Property of congruent | ||

b. | reflexive Property of congruent | ||

c. | definition of congruent angles | ||

d. | substitution Property |

[Definition of congruent angles.]

Correct answer : (3)

5.

$\angle $1 and $\angle $2 are complementary angles. Which of the following statements can be used to say: $\angle $1 + $\angle $2 = 90^{o} ?

a. | definition of complementary angles | ||

b. | angle addition postulate | ||

c. | definition of right angle | ||

d. | definition of supplementary angles |

[Definition of complementary angles.]

Correct answer : (1)

6.

It is given that $m$$\angle $A = 90 and $m$ $\angle $B = 90 . Which of the following is the reason for the statement: $m$$\angle $A = $m$$\angle $B ?

a. | transitive Property | ||

b. | definition of congruent angles | ||

c. | symmetric Property | ||

d. | associative Property |

[Transitive Property.]

Correct answer : (1)

7.

Write the first step of an indirect proof of the following statement:

$\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{CD}}\end{array}$ are perpendicular lines.

$\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{CD}}\end{array}$ are perpendicular lines.

a. | assume $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{CD}}\end{array}$ are parallel lines | ||

b. | assume $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{CD}}\end{array}$ are not perpendicular lines | ||

c. | assume $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{CD}}\end{array}$ are skew lines | ||

d. | assume $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{CD}}\end{array}$ are perpendicular lines |

So, Assume

[Step 1.]

Correct answer : (2)

8.

Find the value of $x$.

a. | 15 | ||

b. | 14 | ||

c. | 12 | ||

d. | 10 |

[Angle addition postulate.]

9

[Simplify.]

[Solve for

Correct answer : (4)

9.

Find the value of $x$.

a. | 27 | ||

b. | 28 | ||

c. | 26 | ||

d. | 29 |

[Definition of a linear pair.]

(2

[Solve for

Correct answer : (1)

10.

Write the first step of an indirect proof of the following statement:

$\angle $A is not a right angle.

$\angle $A is not a right angle.

a. | assume $\angle $A is an acute angle | ||

b. | assume $\angle $A is an obtuse angle | ||

c. | assume $\angle $A is not a right angle | ||

d. | assume $\angle $A is a right angle |

So, Assume

[Step 1.]

Correct answer : (4)