Properties of a Parallelogram
- Author:
- Megan de Jager
Exploration Instructions
1. A parallelogram has been constructed using parallel lines. Use the “move” tool to drag the vertices and change the shape of the parallelogram. (C won’t move but A, B, and D should)
2. Find the measures of the 4 interior angles of parallelogram ABCD using the angle measure tool
and record them below. (To use the tool: select three points or two lines)
_______________ _______________
_______________ _______________
3. Which pairs of angles are opposite angles? What do you notice about the measures of those angles?
4. If you move the points (go back to “Move” tool for this), is your observation about opposite angles still true?
Make a conjecture regarding how opposite angles of a parallelogram are related.
(What do you think is always true of opposite angles in a parallelogram?)
Opposite angles of a parallelogram are ________________________
5. Which pairs of angles are consecutive angles? What do you notice about the measures of those angles?
6. If you move the points, is your observation about consecutive angles still true?
Make a conjecture regarding how consecutive angles of a parallelogram are related.
Consecutive angles of a parallelogram are ________________________
7. Recall that a parallelogram is a quadrilateral in which opposite sides are parallel. Use what you know about parallel lines to explain why you believe that your conjectures in #5 and #7 are true.
8. Use the “distance or length” tool to find the lengths of the four sides of parallelogram ABCD and record them below. (To use the tool: select two points or a segment)
_______________ _______________
_______________ _______________
9. Which pairs of sides are opposite sides?
10. Compare the lengths of opposite sides above and make a conjecture regarding how the opposites sides of a parallelogram are related.
Opposite sides of a parallelogram _________________________________
11. Use the segment tool to draw two diagonals of your parallelogram (connect A to C and B to D).
Use the intersect tool to place point E at the intersection of the diagonals.
12. Use the distance/length tool to measure the interior segments of parallelogram ABCD and record them below. (To ensure an accurate measure, click the two endpoints—like A and E for AE—rather than just the segment.)
_______________ _______________
_______________ _______________
13. What do you notice about AE and CE? How does point E relate to diagonal AC?
14. What do you notice about BE and DE? How does point E relate to diagonal BD?
15. Use your answers for #13, #14, and #15 and your geometric knowledge to fill in the missing word in the following sentence:
If a quadrilateral is a parallelogram, then its diagonals _____________ each other.