Lesson Designed By:

Edited by:

TOPIC:

DISCOVERY LESSON: Fixed Area of a Triangle

LEVEL:

GEOMETER'S SKETCHPAD PROFICIENCY:

CLASS TIME:

GEOMETER'S SKETCHPAD SKILLS NEEDED:

Students should be familiar with the CONSTRUCT and MEASURE menus.

NOTES TO TEACHER:

INVESTIGATION: Fixed Area of a Triangle

PROBLEM:

If the base of a triangle remains the same and the 3rd vertex is moved along a line parallel to the base, what happens to the area of the ever changing triangle?

PROCEDURE:

1 Draw a line and a point above the line.

2. Construct a line through the point which is parallel to your original line.

3. Hide ALL points.

4. Construct points A and B on the lower line and point C on the other line.

5. Connect the 3 points A, B and C to form a triangle. Be sure to draw in AB.

6. Construct the polygon ABC. Color it yellow.

7. Construct another point on the line containing point C. Label it DRAG POINT.

8. Draw a triangle using AB as the base and the DRAG POINT as the 3rd vertex.

9. Construct the polygon interior for the new triangle. Color it red.

RESPOND TO THE QUESTIONS BELOW ON A SHEET OF PAPER:

1. Make a prediction about the areas of the two triangles.

2. Measure the areas of both triangles. Was your conjecture for #1 correct?

3. Change the size and shape of the red triangle by moving the DRAG POINT. How do the areas compare now? What about their perimeters?

4. Construct a chart to display your data concerning the area and perimeter.

5. Animate the DRAG POINT on the line containing C. Stop it periodically and add the new measurements to your chart.

6. What seems to be true about these 2 triangles? Any idea why this happens?

7. Construct a line through C which is perpendicular to AB. Label the point of intersection X.

8. What is CX called?

9. How could you use CX to find the area of each triangle? What formula did you use?

The figure below shows how their final sketch should appear.