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Geometry



Activity:

Properties of Parallelograms

Posted on Feb 7, 2008

Topic: Quadrilaterals & General Polygons

In this activity, students find angle measures and lengths of sides and diagonals of parallelograms, rectangles, rhombi, and squares. They change the size and shape of each type of parallelogram to see which properties hold true for each.

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Activity Key Steps:


Students are to find the length of each side of the parallelogram by using the Length tool (MENU > Measurement > Length). With the Length tool activated, they can find the distance of a side by clicking on each endpoint of the segment.


Students can now drag vertices and watch the measures of the sides as the shape of the parallelogram changes. They need to make a conjecture about the lengths of opposite sides of a parallelogram.


Students are to then measure each angle of the parallelogram (MENU > Measurement > Angle). To measure an angle, select three points on the angle, one on one side of the angle, then the vertex, and then a point on the other side.

Again, students can drag vertices and make a conjecture about the measures of the opposite angles of a parallelogram.


Students will not have difficulty seeing that the opposite angles are congruent, but they may have difficulty recognizing that the consecutive angles are supplementary. Students need to use the Calculate tool (MENU > Tools > Calculate) to find the sum of two consecutive angles. To use the Calculate tool, select the expression (A + B in this case), then the measure of A, and then the measure of B.

Students will see that even as vertices are dragged around, that the consecutive angles always have a sum of 180 degrees.