Parallel Lines: Proving lines are parallel

Numbering in the drawing Identifying and defining elements

Question 1

Given: $3\alpha=x$

Are they parallel lines?

Question 2

Are the lines parallel?

Question 3

Are the lines parallel?

Question 4

For which value of X are the lines parallel?

Question 5

For what value of X are the lines parallel?

Examples with solutions for Parallel Lines: Proving lines are parallel

Exercise #1

Given: $3\alpha=x$

Are they parallel lines?

Video Solution

Step-by-Step Solution

If the lines are parallel, the two angles will be equal to each other, since alternate angles between parallel lines are equal to each other.

We will check if the angles are equal by substituting the value of X:

$x+\alpha+31=3\alpha+\alpha+31=4\alpha+31$

Now we will compare the angles:

$4\alpha+31=4\alpha+29$

We will reduce on both sides to $4\alpha$ We obtain:
$31=29$

Since this theorem is not true, the angles are not equal and, therefore, the lines are not parallel.

Answer

Exercise #2

Are the lines parallel?

Video Solution

Answer

Yes

Exercise #3

Are the lines parallel?

Video Solution

Answer

Exercise #4

For which value of X are the lines parallel?

Video Solution

Answer

$16$

Exercise #5

For what value of X are the lines parallel?

Video Solution

Answer

$2$

Question 1

Lines a and b are parallel.

Lines c and d are parallel.

Are lines a and d parallel?

Question 2

Look at the figure below.

Which lines are are the parallel?

What are the sizes of the marked angles?

Question 3

What is the relationship between a and b given that the lines are parallel?

Exercise #6

Lines a and b are parallel.

Lines c and d are parallel.

Are lines a and d parallel?

Video Solution

Answer

Yes

Exercise #7

Look at the figure below.

Which lines are are the parallel?

What are the sizes of the marked angles?

Video Solution

Answer

a,c parallel $\alpha=120$ $\beta=50$

Exercise #8

What is the relationship between a and b given that the lines are parallel?

Video Solution

Answer

a = 145-3b