# Practice with Rays and Angles

- Author:
- Mr. Marasco, Austen Meek, Yoong Kheong

## Introduction

Last week we learned about rays, angles, and different types of angle relationships. We learned how to find the value of specific angles when we are given related angles. This lesson will be about how to draw them and find them on Geogebra. It is about how to use the software to help us find different angles.

## Rays and Angles Refresher

## Instructions for Constructing a Ray and Angle

1. Click the 3rd icon at the top, which looks like a line tool, then click the 4th icon which looks like a ray tool.
2. Next click anywhere on the graph and then click again anywhere else on the graph to construct your ray.
3. Name the points by clicking the last icon to the right and clicking the "ABC" icon.
- Name the end of the ray point A
NOW YOU HAVE A RAY.
5. Now, construct another ray using the endpoint from the first ray for the endpoint as your second ray.
- Name the new ray you just made (Name the new point on the other ray.
6. Now construct an angle. Just like we name an angle with three points, we also have to make the angle using three points. Click the 8th icon to the right (3rd to last) and click the first icon that has a highlighted angle between two rays.
7. Click on the three points (REMEMBER THE SECOND POINT YOU CLICK MUST BE THE VERTEX, JUST LIKE WE NAME THE ANGLES). ALSO, click the points in a counter clockwise form to get the angle between the rays.
8. Construct an acute angle.

## Question 1

What is the degree of your angle? Why is it acute?

## Question 2

What is the difference between acute, right, and obtuse angles?

## Constructing Angle Bisector

1. Click the 3rd icon at the top, which looks like a line tool, then click the 4th icon which looks like a ray tool.
2. Next click anywhere on the graph and then click again anywhere else on the graph to construct your ray.
3. Name the points by clicking the last icon to the right and clicking the "ABC" icon.
- Name the end of the ray point A
NOW YOU HAVE A RAY.
5. Now, construct another ray using the endpoint from the first ray for the endpoint as your second ray.
- Name the new ray you just made (Name the new point on the other ray.
6. Now construct an angle. Just like we name an angle with three points, we also have to make the angle using three points. Click the 8th icon to the right (3rd to last) and click the first icon that has a highlighted angle between two rays.
7. Click on the three points (REMEMBER THE SECOND POINT YOU CLICK MUST BE THE VERTEX, JUST LIKE WE NAME THE ANGLES)
8.

## Question 3

What do you notice about the two newly made angles? What happens if you move the lines around?

## Observe the Diagram

## Question 4

Name a set of vertical angles.

## Question 5

What type of angles are angle ACF and angle FCE? What do that add up to?

## Question 6

If the measure of angle ACB = 7x and the measure of angle ACF = 13x+20, what is the value of angle FCE?

## Only if you get through the rest of the activity!!

## Question 7

What are complementary angles?

## Question 8

What are supplementary Angles?

## Question 9

What type of angles is a linear pair?

## Question 10: MUST COMPLETE

Did you enjoy this type of lesson? Why? Or why not?