Have you ever had a math question that you couldn't figure out? Take a look at this dilemma.
Candice saw the following illustration in her math book.
She wondered how to describe the relationship between the brown plane and the green plane.
Do you know how to identify this relationship? This Concept will teach you how to help Candace with her dilemma.
In other math classes, you learned about different types of lines. Lines exist in space. Two lines intersect when they cross each other. Because all lines are straight, intersecting lines can only cross each other once.
There are parallel lines, intersecting lines and perpendicular lines. Let’s start by briefly reviewing these terms and then we can look at the angles formed when these lines intersect.
Types of Lines
Parallel Lines are lines that are an equal distance apart. This means that these lines will never intersect.
Intersecting lines are lines that cross at some point.
Perpendicular lines are lines that intersect at a 90∘ angle.
Answer each question.
Lines that will never cross are called?
Solution: Parallel lines
Lines that meet at a 90∘are called?
An intersection is an example of what type of lines?
Solution: Intersecting lines
Now let's go back to the dilemma from the beginning of the Concept.
If you look at these two planes, you will see that they are equidistant. This means that they are the same distance apart and will never intersect. Because these two planes will never intersect, we can say that they are parallel.
This is our answer.
lines that are an equal distance apart and will never intersect.
lines that cross at one point.
lines that intersect at a 90∘ angle and form two or more 90∘ angles.
the measure of the space formed by two intersecting lines.
is a straight line equal to 180∘.
Here is one for you to try on your own.
What is the relationship between ∠STC and ∠ATC?
These two angles meet at a right angle, and so the value of each angle is 90∘. Therefore, the angles are perpendicular angles.
This is our answer.
Parallel and Perpendicular Lines and Planes
Directions: Name each type of lines shown below.
Directions: Write the definitions for the following types of lines.
- Parallel lines
- Intersecting lines
- Perpendicular lines
Directions: Answer the following questions about different types of lines.
- What is the symbol for parallel lines?
- What is the symbol for perpendicular lines?
- An intersection on a highway is an example of what type of lines?
- A four way stop is an example of what type of lines?
- Is it possible for intersecting lines to also be considered perpendicular?
Directions: Describe the types of lines shown in each illustration.