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Rhombi & Squares OH My!

Author:dedmonds
Topic:Geometry

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Exploration 5: Rhombus (15 points)

Plot the following points to create quadrilateral ABCD. A(0,0); B(3,4);C(8,4);D(5,0) Use the line tool to create segments AB, BC, CD and DA.

1. Use the slope and length tools to find the slope and length of each side of the quadrilateral. What do you notice about the slopes of opposite sides? What do you notice about the lengths of opposite sides?

2. Use the measurement tool to find the angle measurement for each angle of the quadrilateral. What do you notice about the measurement of the angles? What can you say about all the angles?

3. Use the line tool to create segment AC and segement BD. Find the length and slope of each segement. Are the diagaonal congruent? Are the diagonals parallel, perpendicular or neither? Justify your answer.

4. Use the point tool to find the intersection of the two diagonals (Point E). Find the length of the each of the four segements the diagaonals were divided. What do you notice about these lengths? What is the relationship bewtween the two diagonals?

5. There are 8 angles created by the diagonals, 2 at each corner of the parallelogram. Use the angle measurement tool to find the measure of each of these angles. What do you notice about these angles? Why is this true?

6. Is every rhombus also a parallelogram? Justify your answer.

7. What additional properties do rhombi have that parallelograms do not have?

Exploration 6: Squares (15 points)

Plot the following points to create quadrilateral ABCD. A(-3,3); B(3,5);C(5,-1);D(-1,-3) Use the line tool to create segments AB, BC, CD and DA.

1. Use the slope and length tools to find the slope and length of each side of the quadrilateral. What do you notice about the slopes of opposite sides? What do you notice about the lengths of opposite sides?

2. Use the measurement tool to find the angle measurement for each angle of the quadrilateral. What do you notice about the measurement of the angles? What can you say about all the angles?

3. Use the line tool to create segment AC and segement BD. Find the length and slope of each segement. Are the diagaonal congruent? Are the diagonals parallel, perpendicular or neither? Justify your answer.

4. Use the point tool to find the intersection of the two diagonals (Point E). Find the length of the each of the four segements the diagaonals were divided. What do you notice about these lengths? What is the relationship bewtween the two diagonals?

5. There are 8 angles created by the diagonals, 2 at each corner of the parallelogram. Use the angle measurement tool to find the measure of each of these angles. What do you notice about these angles? Why is this true?

6. Is every square also a rectangle? Justify your answer?

7. Is every square also a parallelogram? Justify your answer.

8. Is every rhombus also a square? Justify your answer.

9. Is every square also a rhombus? Justify your answer.

7. What additional properties do squares have that rectangles and parallelograms do not have?

Complete the worksheet for Rhombi and Squares (16 points) Check your progress in with Mrs. Edmonds.

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