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 |

[Figure.]

120°, 60° are supplementary.

[As their sum is 180°.]

So, from the converse of same - side interior angles theorem

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 |

So, from the converse of alternate interior angle theorem,

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 |

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 $\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 |

[Figure.]

Since the lines

Correct answer : (4)

5.

[Figure.]

Prove:

The two column proof can be given as follows .

Correct answer : (0)

6.

ABCD is a trapezoid. Prove $x$ = 60.

[Figure.]

Prove:

The two column proof can be given as follows .

Correct answer : (0)

7.

[Figure.]

Prove:

The two column proof can be given as follows

Correct answer : (0)

8.

[Figure.]

Prove: ABDC is a trapezoid .

The two column proof can be given as follows

Correct answer : (0)

9.

[Figure.]

Prove:

The two column proof can be given as follows

Correct answer : (0)

10.

[Figure.]

Prove:

The two column proof can be given as follows

Correct answer : (0)