PARALLEL LINES WORKSHEET

Problem 1 :

The slopes of the two lines are 7 and (3k + 2). If the two lines are parallel, find the value of k.

Problem 2 :

If the following equations of two lines are parallel, then find the value of k.

3x + 2y - 8  =  0

(5k + 3)x + 2y + 1  =  0

Problem 3 :

Find the equation  of a straight line is passing through (2, 3) and parallel to the line 2x - y + 7  =  0. 

Problem 4 :

Verify, whether the following equations of two lines are parallel.

3x + 2y - 7  =  0

y  =  -1.5x + 4 

Problem 5 :

Verify, whether the following equations of two lines are parallel.

5x + 7y - 1  =  0

10x + 14y + 5  =  0

Problem 6 :

In the figure given below,  let the lines l1 and l2 be parallel and m is transversal. If F  =  65°, find the measure of each of the remaining angles.

Problem 7 :

In the figure given below,  let the lines l1 and l2 be parallel and t is transversal. Find the value of x.

Problem 8 :

In the figure given below,  let the lines l1 and l2 be parallel and t is transversal. Find the value of x.

Answers

1. Answer :

If two lines are parallel, then their slopes are equal.

3k + 2  =  7

Subtract 2 from each side. 

3k  =  5

Divide each side by 5. 

k  =  5/3

2. Answer :

3x + 2y - 8  =  0

(5k + 3)x + 2y + 1  =  0

If the two lines are parallel, then their general forms of equations will differ only in the constant term and they will have the same coefficients of x and y. 

To find the value of k, equate the coefficients of x. 

5k + 3  =  3

Subtract 3 from each side. 

5k  =  0

Divide each side by 5.

k  =  0

3. Answer :

Because the required line is parallel to 2x - y + 7 = 0, the equation of the required line and the equation of the given line 2x - y + 7 = 0 will differ only in the constant term.

Then, the equation of the required line is

2x - y + k  =  0 -----(1)

The required line is passing through (2, 3).

Substitute x  =  2 and y = 3 in (1).

2(2) - 3 + k = 0

4 - 3 + k  =  0

1 + k  =  0

k  =  - 1

So, the equation of the required line is

(1)-----> 2x -y - 1  =  0

4. Answer :

3x + 2y - 7  =  0

y  =  -1.5x + 4 

In the equations of the given two lines, the equation of the second line is not in general form. 

Let us write the equation of the second line in general form. 

y  =  -1.5x + 4

1.5x + y - 4  =  0

Multiply by 2 on both sides,

3x + 2y - 8  =  0 

Now, let us compare the equations of two lines, 

3x + 2y - 7  =  0

3x + 2y - 8  =  0

The above two equations differ only in the constant term. 

So, the equations of the given two lines are parallel.

5. Answer :

5x + 7y - 1  =  0

10x + 14y + 5  =  0

In the equation of the second line 10x + 14y + 5 = 0, the coefficients of x and y have the common divisor 2. 

So, divide the second equation by 2

(10x/2) + (14y/2) + (5/2)  =  (0/2)

5x + 7y + 2.5  =  0 

Now, let us compare the equations of two lines, 

5x + 7y - 1  =  0

5x + 7y + 2.5  =  0

The above two equations differ only in the constant term. 

So, the equations of the given two lines are parallel.

6. Answer :

From the given figure, 

F and H are vertically opposite angles and they are equal. 

Then, H  =  F -------> H  =  65°

H and D are corresponding angles and they are equal. 

Then, D  =  H -------> D  =  65°

D and B are vertically opposite angles and they are equal. 

Then, B  =  D -------> B  =  65°

F and E are together form a straight angle.

Then, we have

F + E  =  180°

Plug F  =  65°

F + E  =  180°

65° + E  =  180°

E  =  115°

E and G are vertically opposite angles and they are equal. 

Then, G  =  E -------> G  =  115°

G and C are corresponding angles and they are equal. 

Then, C  =  G -------> C  =  115°

C and A are vertically opposite angles and they are equal. 

Then, A  =  C -------> A  =  115°

Therefore, 

A  =  C  =  E  =  G  =  115°

B  =  D  =  F  =  H  =  65°

7. Answer :

From the given figure, 

(2x + 20)° and (3x - 10)° are corresponding angles. 

So, they are equal. 

Then, we have

(2x + 20)°  =  (3x - 10)°

2x + 20  =  3x - 10

Subtract 2x from each side. 

20  =  x - 10

Add 10 to each side. 

30  =  x

8. Answer :

From the given figure, (3x + 20)° and 2x° are consecutive interior angles. 

So, they are supplementary. 

Then, we have

(3x + 20)° + 2x°  =  180°

3x + 20 + 2x  =  180

Simplify.

5x + 20  =  180

Subtract 20 from each side.

5x  =  160

Divide each side by 8.

x  =  32

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