# USING PROPERTIES OF PARALLEL LINES WORKSHEET

## About "Using properties of parallel lines worksheet"

Using properties of parallel lines worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on properties of parallel lines.

## Using properties of parallel lines worksheet - Problems

Problem 1 :

In the diagram given below, lines m, n and k represent three of the oars. If m||n and n||k, then prove m||k.

Problem 2 :

In the diagram given below, if ∠1 ≅ ∠2, then prove m||n.

Problem 3 :

In the diagram given below, each line is parallel to the next immediate line. Explain why the line K1 is parallel to the line K2.

Problem 4 :

In the diagram given below, lines a and b are perpendicular to the line c. Prove that the lines a and b are parallel.

Problem 5 :

In the diagram given below, if ∠4 and ∠5 are supplementary, then prove g||h.

Problem 6 :

In the diagram given below, find the value of x that makes j||k.

Problem 7 :

If two boats sail at a 45° angle to the wind as shown, and the wind is constant, will their paths ever cross ? Explain.

Problem 8 :

In the diagram given below, decide which rays are parallel.

(i) Is EB parallel to HD ?

(ii) Is EA parallel to HC ?

## Using properties of parallel lines worksheet - Problems

Problem 1 :

In the diagram given below, lines m, n and k represent three of the oars. If m||n and n||k, then prove m||k.

Solution :

 Statements m||n∠1 ≅ ∠2n||k∠2 ≅ ∠3∠1 ≅ ∠3m||k ReasonsGivenCorresponding angles postulateGivenCorresponding angles postulateTransitive property of congruenceCorresponding angle converse

Problem 2 :

In the diagram given below, if ∠1 ≅ ∠2, then prove m||n.

Solution :

 Statements ∠1 ≅ ∠2∠2 ≅ ∠3∠1 ≅ ∠3m||n ReasonsGivenVertical angles theoremTransitive property of congruenceCorresponding angles converse

Problem 3 :

In the diagram given below, each line is parallel to the next immediate line. Explain why the line K1 is parallel to the line K2.

Solution :

We are given that K1||K2 and K2||K3.

By transitive property of parallel lines, K1||K3.

Since K1||K3 and K3||K4, again by transitive property, it follows that K1||K4.

Problem 4 :

In the diagram given below, lines a and b are perpendicular to the line c. Prove that the lines a and b are parallel.

Solution :

Since the line c cuts both the lines a and b, the line c is transversal. Both the lines a and b are perpendicular to the line c. So,  the measure of both ∠1 and ∠2 in the above diagram is 90° and c is transversal to the lines a and b.

That is,

m∠1  =  9

m∠2  =  9

By corresponding angles converse, the lines a and b are parallel.

Problem 5 :

In the diagram given below, if ∠4 and ∠5 are supplementary, then prove g||h.

Solution :

We are given that ∠4 and ∠5 are supplementary. By the linear pair postulate, ∠5 and ∠6 are also supplementary, because they form a linear pair. By the congruence supplements theorem, it follows that ∠4  ∠6. Therefore, by the alternate interior angles converse, g and h are parallel.

Problem 6 :

In the diagram given below, find the value of x that makes j||k.

Solution :

Lines j and k will be parallel if the marked angles are supplementary.

x° + 4x°  =  180°

5x  =  180

x  =  36

So, x = 36 makes j||k.

Problem 7 :

If two boats sail at a 45° angle to the wind as shown, and the wind is constant, will their paths ever cross ? Explain.

Solution :

Because corresponding angles are congruent, the paths of the boats are parallel. Parallel lines do not intersect. So the paths of the boats will never cross.

Problem 8 :

In the diagram given below, decide which rays are parallel.

(i) Is EB parallel to HD ?

(ii) Is EA parallel to HC ?

Solution (i) :

m∠BEH  =  58°

m∠DHG  =  61°

∠BEH and ∠DHG are corresponding angles, but they are not congruent. So EB and HD are not parallel.

Solution (ii) :

m∠AEH  =  62° + 58°  =  120°

m∠CHG  =  59° + 61°  =  120°

∠AEH and ∠CHG are congruent corresponding angles. So AE and CH are parallel.

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