﻿ Properties of Parallel Lines Worksheet | Problems & Solutions

# Properties of Parallel Lines Worksheet

Properties of Parallel Lines Worksheet
• Page 1
1.
If $\stackrel{‾}{\mathrm{AB}}$ || $\stackrel{‾}{\mathrm{CD}}$, $\stackrel{‾}{\mathrm{PR}}$ || $\stackrel{‾}{\mathrm{QS}}$, $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$x$ + $y$

#### Solution:

AB || CD and mCQP = x
[Given.]

mDQF = x
[CQP and DQF are vertical angles.]

Given, PR || QS mEPR = mPQS
[Corresponding Angles Postulate.]

mPQS = 180 - mSQF
[PQF is a straight angle.]

mSQF = mSQD + mDQF

mSQF = y + x
[Substitute mSQD = y, mDQF = x.]

So, mEPR = mPQS = x + y

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.

#### Solution:

If two lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.
[Same side interior angles theorem.]

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

So, the lines a and b are parallel.
[From steps 1 and 2.]

Hence same-side interior angles theorem is used to show that the lines a and b are parallel.

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

#### Solution:

Line n is perpendicular l.
[Given.]

Line n is perpendicular m.
[Given.]

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

So, l and m are parallel.

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.

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. 30o b. 0o c. 90o d. 45o

#### Solution:

The mirror and the line are parallel to each other.

Hence the angle of inclination of the line is 0o.

5.
Six parallel lines are intersected by two lines. How many triangles can be formed?
 a. 5 b. 6 c. 7 d. 12

#### Solution:

Draw six parallel lines and two intersecting lines.

Hence 6 triangles can be formed using all possible ways.

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

#### Solution:

Draw 9 parallel lines with the given distances.

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

7.
ABCD is a trapezoid. Find the value of $x$.

 a. 40 b. 140 c. 60 d. 80

#### Solution:

ADC and DAB are same side interior angles
[DC || AB.]

[Same-Side Interior Angles Theorem.]

(x + 80) + (x - 20) = 180
[Substitute.]

2x + 60 = 180
[Simplify.]

2x = 120
[Rearrange like terms and simplify.]

x = 60
[Solve for x.]

8.
What is $m$$\angle$ADE, if $\stackrel{‾}{\mathrm{DE}}$ || $\stackrel{‾}{\mathrm{BC}}$?

 a. 40 b. 60 c. 70 d. 80

#### Solution:

mABC = 180 - (mBAC + mACB)
[Triangle Angle-Sum Theorem.]

mABC = 180 - (40 + 80)
[Substitute.]

mABC = 60
[Simplify.]

ABC and ADE are corresponding angles.
[DE || BC.]

[Corresponding Angles Postulate.]

[Substitute.]

9.
ED || AB; Find $m$$\angle$EDC. [Given $x$ = 70 and $y$ = 60]

 a. 50 b. 70 c. 130 d. 60

#### Solution:

mCAB = 180 - (mACB + mABC)
[Triangle Angle-Sum Theorem.]

mCAB = 180 - (70 + 60)
[Substitute.]

mCAB = 50
[Simplify.]

EDC and CAB are alternate interior angles
[ED || AB.]

mEDC = mCAB
[Alternate Interior Angles Theorem.]

mEDC = 50
[Substitute.]

10.
ABCD is a parallelogram. Find $m$$\angle$DAB.

 a. 70 b. 110 c. 90 d. 20

#### Solution:

DCB and ABC are same-side interior angles
[DC || AB.]

mABC + mDCB = 180
[Same-Side Interior Angles Theorem.]

DAB and ABC are same-side interior angles

mDAB + mABC = 180
[Same-Side Interior Angles Theorem.]

mDAB + mABC = mABC + mDCB = 180
[Step 2 and Step 4.]

mDAB = mDCB
[Simplify.]

mDAB = 70
[Substitute.]