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Introduction to Parallelograms Using Geogebra

Author:dedmonds
Topic:Geometry

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Exploration 3: Parallelograms (50 points)

3A. Plot the following points to create parallelogram ABCD. A(0,0); B(6,0); C(7,4); D(1,4). Use the line tool to create segments AB, BC, CD and DA.

1. Use the slope tool to find the slope of each side of the parallelogram. What do you notice about the slopes of opposite sides?

2. Use the measurement tool to find the length of each side of the parallelogram. What do you notice about about the lengths of opposite sides?

3. Use the measurement tool to find the angle measurement for each angle of the parallelogram. What do you notice about the measurement of opposite angles?

4. What do you notice about the measurement of any two consecutive angles? Based upon your findings, what do you know about any two consecutive angles of a parallelogram? Why is this true?

5. Create the diagonals for parallelogram ABCD by using the line tool. Create segment AC and find its length and slope. Create segement BD and find its length and slope. Are the diagaonals congruent? Are the diagonals parallel, perpendicular or neither? Justify your answer.

6. Use the point tool to find the intersection of the two diagonals (Point E). Find the length of the each of the four segements the diagaonals were divided. What do you notice about these lengths? What is the relationship between the two diagonals?

7. There are 8 angles created by the diagonals, 2 at each corner of the parallelogram. Use the angle measurement tool to find the measure of each of these angles. What do you notice about these angles? Why is this true?

3B. Plot the following points to create parallelogram ABCD. A(0,0); B(2,4); C(8,6); D(6,2). Use the line tool to create segments AB, BC, CD and DA.

1. Use the slope tool to find the slope of each side of the parallelogram. What do you notice about the slopes of opposite sides?

2. Use the measurement tool to find the length of each side of the parallelogram. What do you notice about about the lengths of opposite sides?

3. Use the measurement tool to find the angle measurement for each angle of the parallelogram. What do you notice about the measurement of opposite angles?

4. What do you notice about the measurement of any two consecutive angles? Based upon your findings, what do you know about any two consecutive angles of a parallelogram?

5. Create the diagonals for parallelogram ABCD by using the line tool. Create segment AC and find its length and slope. Create segement BD and find its length and slope. Are the diagaonals congruent? Are the diagonals parallel, perpendicular or neither? Justify your answer.

6. Use the point tool to find the intersection of the two diagonals (Point E). Find the length of the each of the four segements the diagaonals were divided. What do you notice about these lengths? What is the relationship bewtween the two diagonals?

7. There are 8 angles created by the diagonals, 2 at each corner of the parallelogram. Use the angle measurement tool to find the measure of each of these angles. What do you notice about these angles?

Summarize Your Findings.....

What are the properties of parallelograms that you discovered?

Use your knowledge to complete parallelogram worksheet #1-14. (14 points) Check in w/ Mrs. Edmonds!

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