# In this Geometer’s Sketchpad lesson, equilateral triangles are created and defined

Subjects:

Computers & Internet, Math

3

Title – Classifying Triangles – Equilateral Triangles
By – Kim Ostling
Primary Subject – Math
Secondary Subjects – Computers / Internet

Content:

• A triangle is a three-sided polygon whose interior angles add up to 180 degrees.
• Triangles are classified by either the measure of their sides or the measure of their angles.
• Geometer’s Sketchpad will be used in this lesson to create different triangles and to compare their different parts.

Benchmarks:

• G.GS.03.04 Identify, describe, compare, and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square, and rhombus, based on their component parts (angles, sides, vertices, line segment) and on the number of sides and vertices.

Learning Resources and Materials:

• Journals
• Pencils

Development of Lesson:

• Introduction
• Activate prior knowledge by asking the students:
1. What is a triangle?
2. How many sides does a triangle have?
3. Is there anything we know about the angles of the triangle?
4. Is there anything we know about the sides of a triangle?
5. Is there anything else you would like to share about triangles?
• Methods/Procedures:
• Break the students off into pairs.
• While working in pairs, have the students open Geometer’s Sketchpad.
(Students will have prior experience in working with Geometer’s Sketchpad.)
• Have the students construct an equilateral triangle by following the steps below:
1. Construct a line using the line segment tool.
2. Highlight one endpoint and label it “A” (click on the “Display” menu, then on “Label Point”).
3. Highlight the second endpoint and label it “B”.
4. Select B and the line AB, click on the “Construct” menu and construct a circle with the center B and radius of the line AB.
5. Select the point A and the line segment AB, click on the “Construct menu” and construct a circle with the center A and the radius of the line AB.
6. Label the point where the two circles intersect “C” (click on the “Display” menu, then on the “Label Point”).
7. Construct lines segments AC and BC by using the line segment tool.
8. Click off of the page, then click on the two circles only.
9. Go to “Edit” and select “Action Buttons”, click on the “Hide/Show” button.
10. Click on the new bullet on the page to hide your circles.
11. Click on the line connecting the points A and B, then click on “Measure”, then “Length”.
12. Click on the line connecting the points A and C, then click on “Measure”, then “Length”.
13. Click on the line connecting the points B and C, then click on “Measure”, then “Length”.
• Stop and ask the students:
• What do you notice about the measurement of all three of the sides?
• What happens to the measurement of all three sides when you press on point A and drag?
• What happens to the measurement of all three sides when you press on point B and drag?
1. Click on the points ABC and click on the “Measure”, then “Angle” button.
2. Click on the points BCA and click on the “Measure”, then “Angle” button.
3. Click on the points CAB and click on the “Measure”, then “Angle” button.
• Stop and ask the students:
• What do you notice about the measurement of all three of the angles?
• What happens to the measurement of all three angles when you press on point A and drag?
• What happens to the measurement of all three angles when you press on point B and drag?
• What the students just created is called an “Equilateral Triangle”.
• Together with the students come up with a definition for an equilateral triangle:
• An Equilateral Triangle is a three-sided polygon where all of the sides are equal and all of the angles are congruent to one another.