LESSON #3 Introduction to Angles

Initial lesson posting - July, 2011
Revision date - Fall 2017

Purpose: This lesson introduces the definition of an angle and the common ways in which we classify angles.
Essential Questions: What are the different types of angles? What are a few of the common mistakes students make when discussing angles and their measure?Materials: Protractor and straightedge

A Section of the Lesson Follows

Definition of an angle: Two distinct rays (or segments) with a common endpoint. Angle AVB is shown in figure 3.1
The first ray that is drawn by the turtle is called the initial ray.
The second ray that is drawn by the turtle is called the terminal ray.
Figure3-1.png

The point where the rays (or line segments) meet is the common endpoint for the angle. In figure 3.1, the vertex is labeled with the letter V. Always use upper case letters to label points!
The angle measurement is the number of degrees between these two rays. Some people will call this the magnitude or the amount of turn.
The correct notation for writing angle measure is as follows:
m(AVB) = 50° or m(V) = 50
Use a protractor to verify that the angle shown in figure 3.1 is 50 degrees. If necessary, you may extend the segments with your straight edge tool.

Omitted section of Lesson #3

Example 2:
You can also draw an angle greater than 360 degrees. The following examples show two different ways to draw angle AVB. In figure 3.3, the points A, V and B were printed by using the Turtle Talk or TT command. Note that you only need the double quote mark before the letter.
Figure3-3.jpg
Angles are classified by type (or have specific names) and are measured in degrees with a protractor.
  • An angle equal to 1/4 turn (90° or Pi 2 radians) is called a right angle.
  • Angles equal to 1/2 turn (180° or two right angles) are called straight angles.
  • Angles that are not right angles or multiples of a right angle are called oblique angles.
  • Angles that measure between 0° and 90° are called acute angles ("acute" meaning "sharp").
  • Angles that measure between 90° and 180° (between a right angle and a straight angle) are called obtuse angles ("obtuse" meaning "blunt").
  • Angles that measure between 180° and 360° (between a straight angle and full turn) are called reflex angles.