﻿ Proving Lines are Parallel Worksheet | Problems & Solutions

# 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.

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.

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.

4.
State the postulate or theorem you would use, to prove that $\angle$2 and $\angle$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.

5.
$\angle$1 $\cong$ $\angle$2. Prove $l$ || $m$.

#### Solution:

Given: 1 2
[Figure.]

Prove: l || m.

The two column proof can be given as follows .

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 .

7.
$\angle$ABC = 30°, $\angle$ECD = 30° as shown. Prove: $\stackrel{‾}{\mathrm{BA}}$ || $\stackrel{‾}{\mathrm{CE}}$.

#### Solution:

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

Prove: BA || CE

The two column proof can be given as follows

8.
$\angle$A = 110°, $\angle$B = 110°, $\angle$C = 70°, $\angle$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

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

10.
L1 || L2 || L3 as shown. Prove $\mathrm{a + b}$ = 100.

#### Solution:

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

Prove: a + b = 100

The two column proof can be given as follows