PROPERTIES OF PARALLELOGRAMS

Let us explore the properties of parallelograms by doing the activity below.
Given: AD//BC and AB//DC [br]Manipulates/drag the points A, B, or C for each trial.
Measures of the opposite angles of a parallelogram
A.  Click the box for Show the measure of angles and fill up the table below:[br][br][img]data:image/png;base64,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[/img][br]What can you say about the measures of the opposite angles of a parallelogram?
Measures of the opposite sides of a parallelogram
[br]B. Click the box for Show the side measures and fill up the table below:[br][img]data:image/png;base64,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[/img][br]What can you say about the measures of the opposite sides of a parallelogram?

Information: PROPERTIES OF PARALLELOGRAMS