# Parallelograms: Discovering Properties

1)            Plot and label 2 points A and B anywhere on your screen.  Then construct the line that passes through these 2 points. 2)            Plot and label a point D anywhere that is not collinear with A and B.  (To change the   Name of the point, simply right click on it, choose Rename, and rename it.) 3)             Construct the line passes through points A and D.   4)             Use the Parallel Line tool to construct a line through B that is parallel to AD. 5)             Use the Parallel Line tool to construct a line through D that is parallel to AB. 7)             Use the Intersect tool to plot and label the point of intersection of the lines you’ve constructed in steps (4) and (5).  Label this point C.

How would you classify quadrilateral ABCD?  Why can you classify this quadrilateral this way?

Select (highlight) the entire polygon.  Select the Angle tool to find and display the measures of its four interior angles.

Move any one (or more) of the vertices of this quadrilateral around again.  What do you notice about any one (or more) of its angle measures? Be specific!

1)             In this same file, construct segments AC and BD . 2)             Plot and label a point E at the intersection of these two segments. 3)             Select the Move tool again.   Hide only the segments AC and BD, yet leave point E on the screen.  (Recall you can easily hide any object by right clicking on it and unchecking the “Show Object” icon). 4)             Now use the Segment tool to construct segments AE,  BE, CE, and DE.   5)             Now measure and display the lengths of each of these segments you’ve just constructed.

Move any one (or more) of the vertices of this quadrilateral around again.  The big segments AC and BD are called diagonals of this quadrilateral.  From what you see, what is always true about the diagonals of this quadrilateral?