Subject Area Lessons

## #4254. Area of Triangles

Mathematics, level: Senior
Posted Mon Nov 10 20:18:46 PST 2008 by Cornelia Taran (Cornelia Taran).
Materials Required: Graph paper, Geometer's sketchpad
Activity Time: 50 min

LESSON PLAN FORMAT
Template

Student Teacher's Name: Cornelia Taran
Date: 11-10-2008

Grade Level Geometry Topic/Unit: Area of Triangles School: Pontiac Academy for Excellence District: Pontiac

Content

The students will investigate what happens with the area of a triangle when the base is fixed and the 3rd vertex moves along a line parallel with the base.

Benchmarks

Construct and justify arguments and solve multistep problems involving the area of a triangle.

Learning Resources and Materials
Pre-made graph paper with three triangles (one acute, one obtuse and one right0 with base 4 units and height 3 units.

Development of Lesson
Introduction
Objectives Investigate what happens to area of a triangle when the base is fixed and the third vertex moves along a line parallel to the base

Anticipatory Set The students will receive the pre-made graph paper and asked to find the area of the three triangles.

Lesson What appears to be true about the three triangles? Is this true about any triangle? How can we verify? Work with a partner to answer the questions.

Assess/Evaluate Formative-monitor and provide feedback.

Teacher Directed Instruction. We are going to use Geometer's Sketchpad to verify
the hypothesis.

Methods/Procedures

1. Draw a line and a point above the line.
2. Construct a line through he 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 new measurement to your chart.
6. What seems to be true about these two 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? 