Parallel Lines and Angles Worksheet

**Page 2**

11.

How should the angles 1 and 2 be classified?

a. | Same side interior angles | ||

b. | Alternate interior angles | ||

c. | Corresponding angles | ||

d. | Vertical angles |

Correct answer : (3)

12.

What is the ratio of the number of pairs of same-side interior angles formed by two parallel lines and a tranversal to the number of pairs of alternate interior angles formed by two parallel lines and a transversal?

a. | 1 : 2 | ||

b. | 1 : 1 | ||

c. | 1 : 4 | ||

d. | 2 : 1 |

The two parallel lines and a transversal is as shown.

The pairs of same side interior angles are

Hence two pairs of interior angles are formed.

The pairs of alternate interior angles are

Hence two pairs of alternate interior angles are formed.

The ratio of the number of pairs of same-side interior angles formed by two parallel lines and a tranversal is equal to the number of pairs of alternate interior angles formed by two parallel lines and a transversal = 1 : 1.

Correct answer : (2)

13.

A is a point on line $l$ and B is a point on line $m$. If $l$ is parallel to $m$, is $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ a transversal for lines $l$ and $m$?

a. | No | ||

b. | Yes |

A is a point on line

[As per the question.]

Join the points A and B.

Hence

Correct answer : (2)

14.

Identify the relation between the lines $\begin{array}{c}\overleftrightarrow{\text{ST}}\end{array}$ and $\begin{array}{c}\overleftrightarrow{\text{ZY}}\end{array}$.

a. | skew lines | ||

b. | parallel lines | ||

c. | oblique lines | ||

d. | perpendicular lines |

The lines

Correct answer : (1)

15.

A is a point on line $l$ and B is a point on line $m$. If $l$ intersects $m$ (but not A or B), then which of the following is the most appropriate description for $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$?

a. | bisector to line $l$ and $m$ | ||

b. | perpendicular to line $l$ | ||

c. | perpendicular to line $m$ | ||

d. | transversal of lines $l$ and $m$ |

A is a point on line

[As per the question.]

Hence

Correct answer : (4)

16.

Identify the parallel planes.

a. | $S$$X$$Y$ and $R$$U$$T$ | ||

b. | SXW and TYZ | ||

c. | $S$$T$$U$ and $X$$Y$$T$ | ||

d. | $R$$S$$T$ and $U$$Z$$Y$ |

SXW and TYZ are planes that donot intersect. Hence they are parallel.

Correct answer : (2)

17.

A is a point on line $l$ and B is a point on line $m$. If $l$ and $m$ are skew lines, check if $\begin{array}{c}\overleftrightarrow{\text{AB}}\end{array}$ a transversal for lines $l$ and $m$. Why?

a. | Yes, because the two lines given are not parallel | ||

b. | Yes, because AB intersects the two lines given | ||

c. | Yes, because there are no other lines connecting the two lines given | ||

d. | No, because the two lines given are skew lines |

A transversal is a line that intersects two coplanar lines at two distinct points.

Skew lines are non-coplanar. Hence

Correct answer : (4)

18.

In the figure $\angle $4 and ________ are alternate interior angles.

a. | $\angle $11 | ||

b. | $\angle $10 | ||

c. | $\angle $9 | ||

d. | $\angle $11 |

Hence the alternate interior angles are

Correct answer : (2)

19.

Identify a pair of parallel planes.

a. | UTYZ and WXYZ | ||

b. | STYX and WXYZ | ||

c. | RSXW and RSTU | ||

d. | RSTU and WXYZ |

Planes UTYZ and WXYZ are not parallel as they intersect in line segment YZ.

[Points Y and Z are common to both the planes.]

Planes RSXW and RSTU are not parallel as they intersect in line segment RS.

[Points R and S are common to both the planes.]

Planes STYX and WXYZ are not parallel as they intersect in line segment XY.

[Points X and Y are common to both the planes.]

Planes RSTU and WXYZ are parallel as they do not have any point in common.

Correct answer : (4)

20.

Which of the following is the correct definition of skew lines?

I. Lines that are coplanar and do not intersect.

II. Lines that are coplanar and do intersect.

III. Lines that are neither parallel nor intersecting and are not coplanar.

IV. Lines that lie in the same plane and are parallel.

I. Lines that are coplanar and do not intersect.

II. Lines that are coplanar and do intersect.

III. Lines that are neither parallel nor intersecting and are not coplanar.

IV. Lines that lie in the same plane and are parallel.

a. | III only | ||

b. | IV only | ||

c. | I only | ||

d. | II only |

Skew lines do not lie in the same plane. They are neither parallel nor intersecting.

[From Definition.]

Correct answer : (1)