**Proving lines are parallel worksheet :**

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

**Problem 1 :**

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

**Problem 2 :**

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

**Problem 3 : **

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

**Problem 4 : **

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 5 :**

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

(i) Is EB parallel to HD ?

(ii) Is EA parallel to HC ?

**Problem 1 :**

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

**Solution :**

∠1 ≅ ∠2 ∠2 ≅ ∠3 ∠1 ≅ ∠3 m||n |
Given Vertical angles theorem Transitive property of congruence Corresponding angles converse |

**Problem 2 :**

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 3 : **

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 4 : **

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 5 :**

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.

After having gone through the stuff given above, we hope that the students would have understood "Proving lines are parallel worksheet".

Apart from the stuff given above, if you want to know more about "Proving lines are parallel", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**