Introducing Angles


Objectives: Students will finish exploration from day 1. Students will also learn the properties of and differences between right, acute, and obtuse angles in a new exploration.

Materials: GSP work stations and student worksheet adapted from Exploring Geometry with Geometer's Sketchpad published by Key Curriculum Press


Introducing Angles

NAME:___________________________

An angle is sometimes defined as two rays that share an endpoint. But two segments with a common endpoint also determine an angle. And we usually name an angle after three points. If that's not confusing enough, angle measure is usually considered something different from an angle. In this activity, you'll explore angles and angle measures with Sketchpad.

1. In the Display menu, choose Preferences. Set the angle unit to degrees with precision to the nearest tenth.

2. Use the Ray tool to construct ray AB.

3. Construct another ray AC, with the same endpoint A.

4. Drag each of the three points to make sure the two rays always share a common endpoint (A).

5. If necessary, use the Text toll to display the point labels. Change them to match the figure.

Two rays with a common endpoint form an angle. The common endpoint of the rays is called the vertex of the angle. Name the vertex of the angle you just made.

Answer:____________________________________________________________

 

6. Select, in order, points B, A, and C; then, in the Measure menu, choose Angle.

7. Drag point B or point C and observe how the angle measure changes.

Angles are usually named after three points: a point on one side, the vertex, and a point on the other side. What are two possible names for the angle you just made?

Answer: Angle_________ and Angle___________

 

What's the least angle measure you can make by dragging? What's the greatest?

Answer:____________________________________________________________

 

Drag a point on your angle until the angle's measure is as close to 0 degrees as possible. Describe this angle.

Answer:____________________________________________________________

 

Drag a point on your angle until the angle's measure is as close to 90 degrees as possible. Describe this angle.

Answer:____________________________________________________________

 

Drag a point on your angle until the angle's measure is as close to 180 degrees as possible. Describe this angle.

Answer:____________________________________________________________

 

An acute angle has measure between 0 and 90 degrees. Drag a point on your angle to make it acute. Sketch an example of an acute angle below.

 

 

 

An obtuse angle has measure between 90 and 180 degrees. Drag a point on your angle to make it obtuse. Sketch an example of an obtuse angle below.

 

 

 

A right angle has a measure of exactly 90 degrees. Think back to a previous exercise. What kind of rays make up a right angle?

Answer:____________________________________________________________

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