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Parallel and Perpendicular Lines Worksheet

Parallel and Perpendicular Lines Worksheet
  • Page 1
 1.  
A and B are congruent and supplementary. Prove that A and B are right angles.


Solution:

A two-column proof can be given as shown.

Given: A and B are congruent and supplementary angles.


Prove: A and B are right angles.


Correct answer : (0)
 2.  
What conclusion follows from the following pair of statements?
1. If two non vertical lines are perpendicular, then the product of their slopes is - 1.
2. The product of the slopes of non vertical lines l and n is not - 1.
a.
l is not perpendicular to n
b.
l || n
c.
l n


Solution:

Had l been perpendicular to n, product of their slopes would have been -1.

As product of slopes of l and n is not - 1, it follows that l is not perpendicular to n.


Correct answer : (1)
 3.  
AB CD as shown. Prove: AOC BOC


Solution:

A two-column proof can be given as shown.

Given: AB CD as shown.


Prove: AOC BOC


Correct answer : (0)
 4.  
It is given that mA = mB. Which of the following is the reason for the statement: A B?
a.
transitive Property of congruent
b.
reflexive Property of congruent
c.
definition of congruent angles
d.
substitution Property


Solution:

Two angles are congruent if they have the same measure.
[Definition of congruent angles.]


Correct answer : (3)
 5.  
1 and 2 are complementary angles. Which of the following statements can be used to say: 1 + 2 = 90o ?
a.
definition of complementary angles
b.
angle addition postulate
c.
definition of right angle
d.
definition of supplementary angles


Solution:

Two angles are complementary if the sum of their measures is 90o.
[Definition of complementary angles.]


Correct answer : (1)
 6.  
It is given that mA = 90 and m B = 90. Which of the following is the reason for the statement: mA = mB?
a.
transitive Property
b.
definition of congruent angles
c.
symmetric Property
d.
associative Property


Solution:

If a = b and b = c, then a = c.
[Transitive Property.]


Correct answer : (1)
 7.  
Write the first step of an indirect proof of the following statement:
AB and CD are perpendicular lines.
a.
assume AB and CD are parallel lines
b.
assume AB and CD are not perpendicular lines
c.
assume AB and CD are skew lines
d.
assume AB and CD are perpendicular lines


Solution:

In the first step of an indirect proof, we always assume the opposite of what is to be proved.

So, Assume AB and CD are not perpendicular lines.
[Step 1.]


Correct answer : (2)
 8.  
Find the value of x.


a.
15
b.
14
c.
12
d.
10


Solution:

4 xo + 5 xo = 90o
[Angle addition postulate.]

9xo = 90o
[Simplify.]

x = 10
[Solve for x.]


Correct answer : (4)
 9.  
Find the value of x.


a.
27
b.
28
c.
26
d.
29


Solution:

(2x + 36)o + 90o = 180o
[Definition of a linear pair.]

(2x + 36)o = 90o

x = 27
[Solve for x.]


Correct answer : (1)
 10.  
Write the first step of an indirect proof of the following statement:
A is not a right angle.
a.
assume A is an acute angle
b.
assume A is an obtuse angle
c.
assume A is not a right angle
d.
assume A is a right angle


Solution:

In the first step of an indirect proof, we always assume the opposite of what is to be proved.

So, Assume A is a right angle.
[Step 1.]


Correct answer : (4)

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