﻿ Parallel Lines and Angles Worksheet - Page 2 | Problems & Solutions

# Parallel Lines and Angles Worksheet - Page 2

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

#### Solution:

Two angles are corresponding if they occupy corresponding positions.

1 and 2 occupy corresponding positions. Hence they are corresponding angles.

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

#### Solution:

The two parallel lines and a transversal is as shown.

The pairs of same side interior angles are
4 and 5
3 and 6

Hence two pairs of interior angles are formed.

The pairs of alternate interior angles are
4 and 6
3 and 5

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.

13.
A is a point on line $l$ and B is a point on line $m$. If $l$ is parallel to $m$, is $\begin{array}{c}\stackrel{↔}{\text{AB}}\end{array}$ a transversal for lines $l$ and $m$?
 a. No b. Yes

#### Solution:

A is a point on line j and B is a point on line kand l and m are parallel.
[As per the question.]

Join the points A and B. AB is a transversal.

Hence AB is a transversal.

14.
Identify the relation between the lines $\begin{array}{c}\stackrel{↔}{\text{ST}}\end{array}$ and $\begin{array}{c}\stackrel{↔}{\text{ZY}}\end{array}$.

 a. skew lines b. parallel lines c. oblique lines d. perpendicular lines

#### Solution:

Lines that are not in the same plane and do not intersect are called skew lines.

ST and ZY do not lie in the same plane.

The lines ST and ZY are skew lines.

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 $\begin{array}{c}\stackrel{↔}{\text{AB}}\end{array}$?
 a. bisector to line $l$ and $m$ b. perpendicular to line $l$ c. perpendicular to line $m$ d. transversal of lines $l$ and $m$

#### Solution:

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

A is a point on line l and B is a point on line m. l and m intersects.
[As per the question.]

AB iintersects l and m at two distinct points.

Hence AB is a transversal.

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$

#### Solution:

Parallel planes are planes that donot intersect.

SXY and RUT are planes that intersect. Hence they are not parallel.

RST and UZY are planes that intersect. Hence they are not parallel.

STU and XYT are planes that intersect. Hence they are not parallel.

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

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 $\begin{array}{c}\stackrel{↔}{\text{AB}}\end{array}$ 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

#### Solution:

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

l and m are skew lines. A is a point on line l and B is a point on line m.

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

Skew lines are non-coplanar. Hence AB is not a transversal.

18.
In the figure $\angle$4 and ________ are alternate interior angles.

 a. $\angle$11 b. $\angle$10 c. $\angle$9 d. $\angle$11

#### Solution:

Two angles are alternate interior angles if they lie between the two lines on the opposite sides of the transversal.

4 and 10 lies between two lines on opposite sides of the transversal.

Hence the alternate interior angles are 4 and 10.

19.
Identify a pair of parallel planes.

 a. UTYZ and WXYZ b. STYX and WXYZ c. RSXW and RSTU d. RSTU and WXYZ

#### Solution:

Planes that have no points in common are called parallel planes.

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.

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.
 a. III only b. IV only c. I only d. II only

#### Solution:

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

ST and UV are skew lines.