Proving Lines are Parallel Worksheet

Proving Lines are Parallel Worksheet
  • Page 1
 1.  
State the postulate or theorem you would use, to prove that lines l and m are parallel.


a.
same - side exterior angles theorem
b.
converse of alternate interior angles theorem
c.
converse of same - side interior angles theorem
d.
corresponding angles postulate


Solution:

120°, 60° are same -side interior angles of the transversal.
[Figure.]

120°, 60° are supplementary.
[As their sum is 180°.]

So, from the converse of same - side interior angles theorem l || m.


Correct answer : (3)
 2.  
State the postulate or theorem you would use, to prove that lines m and n are parallel.


a.
same - side exterior angles theorem
b.
converse of corresponding angles postulate
c.
converse of same - side interior angles theorem
d.
converse of alternate interior angles theorem


Solution:

Both the angles are alternate interior angles which are congruent.

So, from the converse of alternate interior angle theorem, m || n.


Correct answer : (4)
 3.  
Select the postulate or theorem that can be used to prove that lines P and Q are parallel.

a.
same - side exterior angles theorem
b.
converse of same - side interior angles theorem
c.
converse of alternate interior angles theorem
d.
converse of corresponding angles postulate


Solution:

Both the angles are alternate interior angles which are congruent.

So, from the converse of alternate interior angles theorem, P || Q.


Correct answer : (3)
 4.  
State the postulate or theorem you would use, to prove that 2 and 3 are congruent.


a.
adjacent angles are congruent
b.
converse of corresponding angles postulate
c.
alternate angles are congruent
d.
corresponding angles postulate


Solution:

3 and 2 corresponding angles.
[Figure.]

Since the lines a and b are parallel from corresponding angles postulate, 3 and 2 are congruent.


Correct answer : (4)
 5.  
1 2. Prove l || m.


Solution:

Given: 1 2
[Figure.]

Prove: l || m.


The two column proof can be given as follows .


Correct answer : (0)
 6.  
ABCD is a trapezoid. Prove x = 60.


Solution:

Given: ABCD is a trapezoid
[Figure.]

Prove: x = 60


The two column proof can be given as follows .


Correct answer : (0)
 7.  
ABC = 30°, ECD = 30° as shown. Prove: BA || CE.


Solution:

Given: ABC = 30°, ECD = 30°.
[Figure.]

Prove: BA || CE


The two column proof can be given as follows


Correct answer : (0)
 8.  
A = 110°, B = 110°, C = 70°, D = 70° as shown. Prove that ABDC is a trapezoid.


Solution:

Given: A = 110°, B = 110°, C = 70°, D = 70°
[Figure.]

Prove: ABDC is a trapezoid .


The two column proof can be given as follows


Correct answer : (0)
 9.  
L1 || L2, L3 || L4 as shown. Prove : x = 60.


Solution:

Given: L1 || L2, L3 || L4
[Figure.]

Prove: x = 60

The two column proof can be given as follows


Correct answer : (0)
 10.  
L1 || L2 || L3 as shown. Prove a + b = 100.


Solution:

Given: L1 || L2 || L3
[Figure.]

Prove: a + b = 100


The two column proof can be given as follows


Correct answer : (0)
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