Properties of Parallel Lines Worksheet

**Page 1**

1.

If $\stackrel{\u203e}{\mathrm{AB}}$ || $\stackrel{\u203e}{\mathrm{CD}}$, $\stackrel{\u203e}{\mathrm{PR}}$ || $\stackrel{\u203e}{\mathrm{QS}}$, $m$$\angle $CQP = $x$ and $m$$\angle $SQD = $y$, then find $m$$\angle $EPR.

a. | $x$ - $y$ | ||

b. | 180 - ($x$ + 2 $y$) | ||

c. | 180 - ($x$ + $y$) | ||

d. | 2$x$ + $y$ |

[Given.]

[

Given, PR || QS

[Corresponding Angles Postulate.]

[

[Substitute

So,

Correct answer : (3)

2.

Which theorem would you use to show that $a$ || $b$?

a. | alternate interior angles theorem | ||

b. | corresponding angles theorem | ||

c. | same-side interior angle theorem | ||

d. | in a plane, if two lines are perpendicular to the same line, then they are parallel to each other. |

[Same side interior angles theorem.]

The two angles are same-side interior angles and are supplementary.

So, the lines

[From steps 1 and 2.]

Hence same-side interior angles theorem is used to show that the lines

Correct answer : (3)

3.

Which theorem can you use to prove that $l$ is parallel to $m$?

a. | if two lines are parallel to the same line, then they are parallel to each other | ||

b. | alternate Interior Angles Converse | ||

c. | cannot prove that $l$ is parallel to $m$ | ||

d. | in a plane, if two lines are perpendicular to the same line, then they are parallel to each other |

[Given.]

Line

[Given.]

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

So,

Hence the satement 'In a plane, if two lines are perpendicular to the same line, then they are parallel to each other' is used to prove that the lines are parallel.

Correct answer : (4)

4.

A line is parallel to its image under reflection by a mirror. The angle at which the line is inclined to the mirror is

a. | 30 ^{o} | ||

b. | 0 ^{o} | ||

c. | 90 ^{o} | ||

d. | 45 ^{o} |

The mirror and the line are parallel to each other.

Hence the angle of inclination of the line is 0

Correct answer : (2)

5.

Six parallel lines are intersected by two lines. How many triangles can be formed?

a. | 5 | ||

b. | 6 | ||

c. | 7 | ||

d. | 12 |

Draw six parallel lines and two intersecting lines.

Hence 6 triangles can be formed using all possible ways.

Correct answer : (2)

6.

There are 9 parallel lines. The distance between the first 5 consecutive lines is 2 cm each, that between the next lines is 3 cm each. What is the distance between the first and the ninth line in cm?

a. | 18 cm | ||

b. | 20 cm | ||

c. | 23 cm | ||

d. | 22 cm |

Draw 9 parallel lines with the given distances.

From the figure, the distance between the first and the ninth line is 20 cm.

Correct answer : (2)

7.

ABCD is a trapezoid. Find the value of $x$.

a. | 40 | ||

b. | 140 | ||

c. | 60 | ||

d. | 80 |

[DC || AB.]

[Same-Side Interior Angles Theorem.]

(

[Substitute.]

2

[Simplify.]

2

[Rearrange like terms and simplify.]

[Solve for

Correct answer : (3)

8.

What is $m$$\angle $ADE, if $\stackrel{\u203e}{\mathrm{DE}}$ || $\stackrel{\u203e}{\mathrm{BC}}$ ?

a. | 40 | ||

b. | 60 | ||

c. | 70 | ||

d. | 80 |

[Triangle Angle-Sum Theorem.]

[Substitute.]

[Simplify.]

[

[Corresponding Angles Postulate.]

[Substitute.]

Correct answer : (2)

9.

a. | 50 | ||

b. | 70 | ||

c. | 130 | ||

d. | 60 |

[Triangle Angle-Sum Theorem.]

[Substitute.]

[Simplify.]

[ED || AB.]

[Alternate Interior Angles Theorem.]

[Substitute.]

Correct answer : (1)

10.

ABCD is a parallelogram. Find $m$$\angle $DAB.

a. | 70 | ||

b. | 110 | ||

c. | 90 | ||

d. | 20 |

[DC || AB.]

[Same-Side Interior Angles Theorem.]

[AD || BC.]

[Same-Side Interior Angles Theorem.]

[Step 2 and Step 4.]

[Simplify.]

[Substitute.]

Correct answer : (1)