Exploring Geometry
Properties of Parallelograms  

 

 

How do I do it

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Select AB and point C; then in the Construct Menu, choose parallel line.

 

 

 

 

 

To measure an angle, select three points, with the vertex selected in the middle. Then, in the Measure menu, choose Angle.

 

Select a segment; then , in Measure menu, choose Length. OR select two points and measure Distance.

 

 

You will be investigating a parallelogram, which is a quadrilateral whose opposite sides are parallel.

  Sketch and Investigate 

  • Construct segment AB and a point C, not on the segment.

  • Construct a line through C parallel to segment AB.

  • Construct segment AC.

  • Construct a line through B parallel to AC.

  • Construct a point D, at the intersection of the two lines.

  • Hide both lines, then finish your parallelogram by constructing segments that form the missing sides.

  • Drag different vertices to make sure that you constructed a parallelogram correctly.

  • Measure the sides and angles of the parallelogram

  • Drag different vertices of your parallelogram and observe the measurements.

  • Construct the diagonals and their points of intersection

  • Drag Parts of the parallelogram and observe the diagonals.  Measure lengths that look as if they might be related.

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Points to Ponder

  • On a separate sheet of paper, write at least three conjectures about the sides and angles of a parallelogram. 
  • Write a conjecture about the diagonals of a parallelogram.  

Going Further & Deeper . . . 
Constructing a Parallelogram

1.     How many ways can you come up with to construct a parallelogram? Try methods that use the Construct menu, the Transform menu, or combinations of both. Consider how you might use diagonals. Write a brief description of each construction method along with the properties of parallelograms that make that method work.

You should do this construction and print it out and include it as part of your "Construction Notebook".