Geometry
Ch. 8: Quadrilaterals
8.2: Investigating Properties of Parallelograms
Name: _________________________________________________
Date: ___________________________________________________
Essential Question: What are unique properties of parallelograms?
Part 1: Drawing a Parallelogram
1. Using the segment tool, draw a segment.
Use the label tool to label the endpoints A and B.
2. Place a point C not on the segment AB.
3. High light points A and C. From the Construct Menu
choose segment. Draw segment AC.
4. Highlight point C and segment AB. From the Construct
Menu choose Parallel line.
5. Highlight point B and segment AC. From the Construct
Menu choose Parallel line.
6. Highlight the two lines you created. From the Construct
Menu choose Intersection. Label the point D.
7. Highlight the two lines you created again. From the Display
menu choose Hide Lines. Draw segments CD and BD.
Part 2: Investigating Properties of Parallelograms.
1. Measure the slopes of all four sides of the parallelogram. Highlight a side, from the Measure Menu
choose slope. Next highlight the side opposite and find it’s slope. Do the same for the last 2 sides.
Complete the Chart below.
Segment
Slope
Question: What do you notice about the slopes of opposite sides of a parallelogram?
Make a conjecture:
Opposite sides have _________________________ slopes; so opposite sides are _____________________.
2. Measure the lengths of all four sides. Highlight a side. From the Measure Menu, choose length. Next
highlight the side opposite and find it’s length. Do the same for the last 2 sides. Complete the Chart
below.
Side
Length
Question: What do you notice about the lengths of opposite sides of a parallelogram?
Make a conjecture:
Opposite sides of a parallelogram are _________________________.
3. Measure all four angles. Highlight 3 points. From the Measure Menu, choose angle. Do the same for
the remaining 3 angles and fill out the chart below.
Angle
Measure
a.) From the Number Menu, choose calculate to get a calculator. Find the sum of the 2 pairs of
adjacent angles.
Question: What do you notice about the opposite angles of a parallelogram? What do you notice
about adjacent angles of a parallelogram?
Make a conjecture:
Opposite angles of a parallelogram are _________________________, Adjacent angles ______________________________.
b.) Drag one vertex of the parallelogram to change its shape. Do your conjectures from 1, 2,
and 3 hold true?
4. Draw diagonals AD and BD. Highlight the end points. From the Construct Menu, choose segment.
Highlight each diagonal you just drew. From the Construct Menu choose intersection. Label your
point of intersection.
5.Measure the length of each diagonal. Highlight the diagonal. From the Measure Menu, choose
length.
Question: Are the lengths of the diagonals the same?
6. Highlight point A and point E. From the Measure Menu, choose length. Do the same for the
remaining parts of each diagonal. Complete the chart below.
Segment
Length
Make a conjecture:
The diagonals of a parallelogram _____________________________________ each other.
Part 3: Draw Conclusions.
1. Based on your investigation, list 4 properties of parallelograms.
a.)____________________________________________________________________________________________________________
b. )____________________________________________________________________________________________________________
c.)____________________________________________________________________________________________________________
d.)____________________________________________________________________________________________________________