Properties of Parallelograms
A parallelogram is a quadrilateral whose opposite sides are parallel. In this activity you will construct a parallelogram using the definition, then investigate properties of parallelograms.
1. Construct (
) and point above the segment (
).
2. Construct a line through parallel to . To do this, click the 
Perpendicular Line tool, then choose 
Parallel Line. Click on and .
3. Construct .
) and point above the segment ().
2. Construct a line through parallel to . To do this, click the Perpendicular Line tool, then choose Parallel Line. Click on and .
3. Construct .
4. Construct a line through parallel to .
5. Construct point , the intersection of the two lines, by clicking the Point menu, then 
Intersect, then clicking on each line.
6. Hide both lines by ctrl-clicking and un-checking Show Object from the contextual menu. Finish your parallelogram by constructing the missing segments.
7. Drag different vertices of your parallelogram to make sure it's constructed properly.
8. Measure the sides and angles of the parallelogram. To measure the sides, click the 
Angle menu, then choose 
Distance or Length and click on the sides. To measure the angles, choose Angle, then click three points with the vertex in the middle.
9. Drag different parts of the parallelogram and observe the measurements.
Point menu, then Intersect, then clicking on each line.
6. Hide both lines by ctrl-clicking and un-checking Show Object from the contextual menu. Finish your parallelogram by constructing the missing segments.
7. Drag different vertices of your parallelogram to make sure it's constructed properly.
8. Measure the sides and angles of the parallelogram. To measure the sides, click the Angle menu, then choose Distance or Length and click on the sides. To measure the angles, choose Angle, then click three points with the vertex in the middle.
9. Drag different parts of the parallelogram and observe the measurements.Q1
Write a conjecture about the sides or angles of a parallelogram.
Q2
Write a second conjecture about the sides or angles of a parallelogram.
Q3
Write a third conjecture about the sides or angles of a parallelogram.
10. Construct the diagonals and their point off intersection.
11. Drag parts of the parallelogram and observe the diagonals. Measure any lengths that look like they might be related. You can measure the distance between any two points by clicking Distance or Length, then clicking both points.
Distance or Length, then clicking both points.Q4
Write a conjecture about the diagonals of a parallelogram.
Q5
Investigate the symmetry of the parallelogram. Does it have reflection symmetry? If so, where is the line of symmetry located? Does it have rotation symmetry? If so, by what angle?
After you complete this activity, please copy your conjectures from above into the "Properties of Parallelograms" discussion in Schoology and submit your post.