Parallelograms: Discovering Properties

1)            Plot and label 2 points A and B anywhere on your screen.  Then construct the line that [br]passes through these 2 points. [br] [br]2)            Plot and label a point D anywhere that is not collinear with A and B.  (To change the  [br]Name of the point, simply right click on it, choose Rename, and rename it.) [br] [br]3)             Construct the line passes through points A and D.  [br][br]4)             Use the Parallel Line tool to construct a line through B that is parallel to AD. [br] [br]5)             Use the Parallel Line tool to construct a line through D that is parallel to AB.[br] [br]7)             Use the Intersect tool to plot and label the point of intersection of the lines you’ve[br]constructed in steps (4) and (5).  Label this point C. [br]
How would you classify quadrilateral ABCD?  Why can you classify this [br]quadrilateral this way?
Select (highlight) the entire polygon.  Select the Angle tool to find and display the [br]measures of its four interior angles.   [br] [br][br][br]
Move any one (or more) of the vertices of this quadrilateral around again.  What do you[br]notice about any one (or more) of its angle measures? Be specific!
1)             In this same file, construct segments AC and BD .[br] [br]2)             Plot and label a point E at the intersection of these two segments.[br] [br]3)             Select the Move tool again.   Hide only the segments AC and BD, yet leave point E on [br]the screen.  (Recall you can easily hide any object by right clicking on it and unchecking [br]the “Show Object” icon). [br] [br]4)             Now use the Segment tool to construct segments AE,  BE, CE, and DE.  [br] [br]5)             Now measure and display the lengths of each of these segments you’ve just [br]constructed. [br] [br]
Move any one (or more) of the vertices of this quadrilateral around again.  The big [br]segments AC and BD are called diagonals of this quadrilateral.  From what you see, [br]what is always true about the diagonals of this quadrilateral?
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