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.
[math][/math]1. Construct [math]\overline{AB}[/math] ([icon]/images/ggb/toolbar/mode_segment.png[/icon]) and point [math]C[/math] above the segment ([icon]/images/ggb/toolbar/mode_point.png[/icon]).[br][br]2. Construct a line through [math]C[/math] parallel to [math]\overline{AB}[/math]. To do this, click the [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon] [b]Perpendicular Line[/b] tool, then choose [icon]/images/ggb/toolbar/mode_parallel.png[/icon] [b]Parallel Line[/b]. Click on [math]\overline{AB}[/math] and [math]C[/math].[br][br]3. Construct [math]\overline{AC}[/math].
4. Construct a line through [math]B[/math] parallel to [math]\overline{AC}[/math].[br][br]5. Construct point [math]D[/math], the intersection of the two lines, by clicking the [icon]/images/ggb/toolbar/mode_point.png[/icon][b] Point[/b] menu, then [icon]/images/ggb/toolbar/mode_intersect.png[/icon] [b]Intersect[/b], then clicking on each line.[br][br]6. Hide both lines by ctrl-clicking and un-checking [i]Show Object[/i] from the contextual menu. Finish your parallelogram by constructing the missing segments.[br][br]7. Drag different vertices of your parallelogram to make sure it's constructed properly.[br][br]8. Measure the sides and angles of the parallelogram. To measure the sides, click the [icon]/images/ggb/toolbar/mode_angle.png[/icon] [b]Angle[/b] menu, then choose [icon]/images/ggb/toolbar/mode_distance.png[/icon] [b]Distance or Length[/b] and click on the sides. To measure the angles, choose [icon]/images/ggb/toolbar/mode_angle.png[/icon] [b]Angle[/b], then click three points with the vertex in the middle.[br][br]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.[br][br]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 [icon]/images/ggb/toolbar/mode_distance.png[/icon][b] Distance or Length[/b], 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.