Parallel Lines - Examples, Exercises and Solutions

In drawing B, we observe two right angles, which teaches us that they are practically equal. From this, we can conclude that they are corresponding angles, located at the intersection of two parallel lines.

In drawing A, we only see one right angle, so we cannot deduce that the two lines are parallel.

Let's first think about the different definitions of various lines.

We can see that what is common to all of the lines is that they intersect each other, meaning they have a point of intersection.

Remember that lines that cross each other are lines that will meet at a certain point.

Therefore, the correct answer is (a).

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where it can be seen that the lines form a right angle of 90 degrees between them is drawing A.

Let's remember the different properties of lines.

The lines are not parallel since they intersect.

The lines are not perpendicular since they do not form a right angle of 90 degrees between them.

Therefore, no answer is correct.

Lines that intersect each other are lines that meet or cross each other.

The diagrams showing lines that cross each other are 1 and 3.

In diagram 2, the lines are perpendicular and vertical to each other, while in drawing 4, the lines are parallel to each other.

Parallel lines are lines that, if extended, will never meet.

In the drawings A+B+D if we extend the lines we will see that at a certain point they come together.

In drawing C, the lines will never meet, therefore they are parallel lines.

Perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where the lines form a right angle of 90 degrees between them is drawing A.

Upon observation we can see that all the lines form a right angle of 90 degrees with each other.

Typically lines that form a right angle of 90 degrees with each other are perpendicular and vertical lines.

Therefore, the correct answer is a.

Upon observation we can see that all the lines intersect forming a right angle of 90 degrees.

Typically intersecting lines that form a right angle of 90 degrees are perpendicular and vertical lines.

Therefore, the correct answer is a.

Remember that parallel lines are lines that, if extended, will never intersect.

In diagrams a'+b'+c', all the lines intersect with each other at a certain point, except for diagram d'.

The lines drawn in answer d' will never intersect.

Remember the properties of parallel lines.

Since there is no connection between the size of the line and parallelism, the lines are indeed parallel.

Let's think about the different types of lines.

Looking at side AB and side CD, we can see that if we extend both of them, they will never intersect.

Also, according to the properties of a rectangle, each pair of opposite sides are parallel to each other.

Therefore, the answer is correct and indeed AB is parallel to CD.

The two pairs of opposite sides are parallel because the two rectangles are connected to form a square, creating a 90-degree angle.

Therefore, the opposite sides in the drawing must be parallel.

For the lines to be parallel, the two angles must be equal (according to the definition of corresponding angles).

Let's compare the angles:

$2x+10=70-x$

$2x+x=70-10$

$3x=60$

$x=20$

Once we have worked out the variable, we substitute it into both expressions to work out how much each angle is worth.

First, substitute it into the first angle:

$2x+10=2\times20+10$

$40+10=50$

Then into the other one:

$70-20=50$

We find that the angles are equal and, therefore, the lines are parallel.

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.