Properties of Parallelograms
(A discovery lesson plan using Geometer’s Sketchpad
Designed by Rebecca A. Zeier)
After answering a variety of guided questions about the parallelogram, students should be able to identify the different properties of the parallelogram.
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:
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 _____
Angle ADC _____
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.
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
Are they congruent?
C. Measure the following angles and record your results.
Angle BAE _____
Angle ADE _____
Angle DCE _____
Angle CBE _____
Angle EAD _____
Angle EDC _____
Angle ECB _____
Angle EBA _____
D. What do you notice?
E. Measure the lengths of the following segments
F. What do you notice?
G. Calculate the slopes of the following segments
H. What do you notice?
I. Make conjectures about the properties of the diagonals of a parallelogram.
A. List as many properties of the parallelogram as you can
B. Now wasn’t that FUN???