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Properties of Parallel Lines Worksheet

Properties of Parallel Lines Worksheet
  • Page 1
 1.  
If AB || CD, PR || QS, mCQP = x and mSQD = y, then find mEPR.

a.
x - y
b.
180 - (x + 2 y)
c.
180 - (x + y)
d.
2x + 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


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.


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.


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


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.


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.
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.


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


Solution:


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


Solution:


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


Solution:

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

mADC + mDAB = 180
[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.]


Correct answer : (3)
 8.  
What is mADE, if DE || 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.]

mADE = mABC
[Corresponding Angles Postulate.]

mADE = 60
[Substitute.]


Correct answer : (2)
 9.  
ED || AB; Find mEDC. [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.]


Correct answer : (1)
 10.  
ABCD is a parallelogram. Find mDAB.

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
[AD || BC.]

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

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

mDAB = mDCB
[Simplify.]

mDAB = 70
[Substitute.]


Correct answer : (1)

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