Properties of Parallelograms

Construct the geometric object by following the instructions below, and then answer the questions about the object. 
  1. Create a parallelogram. 
    1. Construct segment AB. 
    2. Construct a line above AB parallel to it. 
    3. Label a point at the left end of the new line D. 
    4. Construct segment AD. 
    5. Construct a line parallel to AD through point B. 
    6. Find the intersection point and label it C. 
    7. From the Draw Toolbar, select Hide/Show. 
    8. Move to line BC until the message This line appears. Click once. A dotted line appears. 
    9. Move to line CD until the message This line appears. Click once. A dotted line appears. 
    10. Construct segment CD and BC. 


      11. Figure 9.1

  2. Find and label the lengths of all the sides. 
  3. What is the relationship between opposite sides AD and BC?

    4. ___________________________________ 
  4. What is the relationship between opposite sides AB and CD?

    5. ___________________________________ 
  5. Alter parallelogram ABCD. 
    1. From the Points Toolbar, select Pointer. 
    2. Move to point A until the message This point appears. Click once and drag. 
  6. Is the relationship between the opposites sides the same?

    7. ___________________________________ 
  7. Alter the parallelogram several times by using the pointer to see if the results change. If they do, under what conditions?

    8. ___________________________________ 
  8. What can you conclude about the opposite sides of a parallelogram?

    9. ___________________________________ 
  9. Find and label the measure of each angle. 
  10. What is the relationship between the opposite angles angleA and angleC?

    11. ___________________________________ 
  11. What is the relationship between the opposite angles angleB and angleD?

    12. ___________________________________ 
  12. Alter parallelogram ABCD. 
  13. Is the relationship between the opposite angles the same?

    14. ___________________________________ 
  14. Alter the parallelogram several times by using the pointer to see if the results change. If they do, under what conditions?

    15. ___________________________________ 
  15. What can you conclude about the opposite angles of a parallelogram?

    16. ___________________________________ 
  16. What is the relationship between the consecutive angles angleA and angleB?

    17. ___________________________________ 
  17. What is the relationship between the consecutive angles angleB and angleC?

    18. ___________________________________ 
  18. Alter parallelogram ABCD. 
  19. Is the relationship between the consecutive angles the same?

    20. ___________________________________ 
  20. Alter the parallelogram several times by using the pointer to see if the results change. If they do, under what conditions?

    21. ___________________________________ 
  21. What can you conclude about the consecutive angles of a parallelogram?

    22. ___________________________________ 
  22. Clear the measurements. 
  23. Construct segments AC and BD, which represent the diagonals. 
  24. Find the intersection point and label it M. 


    25. Figure 9.2

  25. Find and label the lengths of segments AM, BM, CM, and DM. 
  26. What is the relationship between the diagonals of parallelogram ABCD?

    27. ___________________________________ 
  27. Alter parallelogram ABCD. 
  28. Is the relationship between the diagonals the same?

    29. ___________________________________ 
  29. Alter the parallelogram several times by using the pointer to see if the results change. If they do, under what conditions?

    30. ___________________________________ 
  30. What can you conclude about the diagonals of a parallelogram?

    31. ___________________________________ 
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