# Parallel and Perpendicular Lines Worksheets

Classifying the relationship that exists between two lines can help us understand a great deal about a system. If they are perfect straight, in relation to one another, this can help you to better understand the angles that forms when a transversal line crosses both of them. When two lines are a fixed distance apart from each other infinitely this relationship is described a parallel. Line that are in this form of relationship will never cross each other. When a line crosses another line at exactly 90 degrees, we describe those lines as being perpendicular. This selection of worksheets and lessons will help students learn how to identify these relationships. In future topics we will learn how to use the information provided by these relationships to better understand an entire planar system.

### Aligned Standard: High School Geometry - HSG-CO.A.1

- What's the Difference between Parallel and Perpendicular? Lesson- We start as basic as it can get. We add intersection as we progress.
- Identifying Perpendiculars Worksheet 1 - Hawk out those right angles right away.
- Parallel, Perpendicular, and Intersecting Worksheet 2 - You are given mish mash of lines. Make sense of them right away.
- Equations of Parallel Worksheet 3 - We start to look at the actual behind the scenes equation behind all of these lines.
- Slopes of Parallel and Perpendicular Worksheet 4 - This is a slightly more advanced sheet to get them thinking.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Start by finding the parallels, work on some equations, and end up right where you started.

- Homework 1 - State whether the given pair of lines are parallel.
- Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting.
- Homework 3 - Determine if the given par of lines is parallel, perpendicular, or intersecting.
- Homework 4 - Where Are the Parallel Lines?

### Practice Worksheets

We cover all the main skills here, but sheets 2 and 3 are more advanced.

- Practice 1 - Determine the classification of the line pairs. You can assume a number of things based on observations.
- Practice 2 - You are given equations to plot and are asked to determine the relation of. You will not even need to graph them.
- Practice 3 - Find the equation of a line passing through the given point and perpendicular to the given equation. Write your answer in slopeāintercept form.
- Practice 4 - You will classify all of these based on what you see.

### Math Skill Quizzes

The quizzes cover the nitty gritty: slope and line pair identification.

- Quiz 1 - Where do these guys fall? Are they special or just in a regular relationship?
- Quiz 2 - For the given slope, find the slope of any parallel and perpendicular line to it.
- Quiz 3 - Everything here is based off of the slopes that are presented to you.

### What are Parallel and Perpendicular Lines?

We see lines going in different directions, don't we? Sometimes they're going upwards, downwards, straight, sideways, or at an angle. Sometimes they meet or cross each other. The purpose of this is to take some time to define the vocabulary of how these lines interact. Let's find out!

**Parallel lines** - Have you seen how the railway tracks run on the ground? They are quite apart from each other and seem like they never meet. Well, that's exactly what parallel means. A set of lines that are on the same distance with each other and don't intersect are called parallel. An easy example to understand better is the "=" sign.

**Perpendicular lines** - You must have seen how a pizza is sliced, right? They are cut from the middle, and sideways. Notice how at the center, they meet? The common endpoint of these lines is known as an angle.

So when one line crosses another forming a 90° angle, they are called perpendicular. An easy example to understand is the "+" sign.

### Why Do These Relationships Help Us to Do?

As you advance forward with geometry and math in general, these relationships will be given or previously stated to you in the problems that you are responsible for. If you can identify that these types of relations exist, it tells you a great deal system that you are evaluating. If you find a parallel series and transversal cutting through both lines, the angles that are formed are quite easy to determine as long as you are given a single angle. It is almost amazing how much the tell about a series that exist in this manner. When you discover a perpendicular, it can help you solve linear equations not to mention simple angle measures. While this may just seem like simple math to you, as you start to build anything with your hands you will learn the weight of these connections that exist. I learned this firsthand when building a simple ten by ten deck off of my house. Geometry of angles is powerful form of math that can be used as a tool to create some awesome structures, I explain this while sitting on my deck. Which was fashioned thanks to geometry!