Properties of Parallelograms

(A discovery lesson plan using Geometer’s Sketchpad

Designed by Rebecca A. Zeier)

Objective:

After answering a variety of guided questions about the parallelogram, students should be able to identify the different properties of the parallelogram.

Activity:

Have the students work independently or in pairs to answer the following questions.

Directions:  Get into Geometer’s Sketchpad Software.

I. Open the file named “parallelogram”

II. Label the angles A, B, C, and D as shown below:

 D C

 B

 A

III. Measure of sides

A. Use the measure tool and measure all four sides of the parallelogram.  Record your results below:

BC _____

CD _____

DA _____

B. What do you notice about the lengths of the sides?

C. Use the “drag” function to change the lengths of the sides.  What do you notice?

D. Using your knowledge of parallel lines (hint: slope), what should be true about the sides of a parallelogram?

E. Use the tool to evaluate slopes to see if you are correct.  Record your results below.

Slope of AB _____

Slope of BC _____

Slope of CD _____

Slope of DA _____

F. Make a conjecture about the properties of the sides of parallelograms.

IV. Measure of Angles

A. Use the measure tool to measure all 4 angles of the parallelogram.  Record your results below.

Angle DAB _____

Angle ABC _____

Angle DCB _____

B. What do you notice about the measures of all the angles?

C. Use the “drag” tool again to change the size of the parallelogram.  What do you notice about the angles?

D. Make a conjecture about the properties of the measures of angles of the parallelogram.

V. Diagonals

A. Use the draw tool to draw in the diagonals.  Label the intersection of the two diagonals as “E”.

B. Use the measure tool to measure the lengths of

BD _____

AC _____

Are they congruent?

C. Measure the following angles and record your results.

Angle BAE _____

Angle DCE _____

Angle CBE _____

Angle EDC _____

Angle ECB _____

Angle EBA _____

D. What do you notice?

E. Measure the lengths of the following segments

AE _____

DE _____

EC _____

EB _____

F. What do you notice?

G. Calculate the slopes of the following segments

AC _____

DB _____

H. What do you notice?

I. Make conjectures about the properties of the diagonals of a parallelogram.

VI. Recap

A. List as many properties of the parallelogram as you can

B. Now wasn’t that FUN???