Ch 7 Extra Credit: Quadrilateral Creation

1. a). Move the vertices of this quadrilateral around to form a PARALLELOGRAM.

1b)

[b] -->[/b] In the applet above, use the SLOPE tool on the left (tap the tool, and then tap each side) to show the slopes of the sides. *Note: if you made any sides vertical, Geogebra won't find the slope -- because there is no slope!*[br][br] [b] (If you need to move your vertices, use the MOVE tool.)[/b][br][br] [b] -->[/b] In the space below, explain how your results confirm that this quadrilateral is a parallelogram by writing the appropriate theorem. [br] [b] (For example: One pair sides congruent and || --> parallelogram)[/b][br]

2a) Move the vertices of this quadrilateral around to form a PARALLELOGRAM.

2b)

[b] -->[/b] In the applet above, use the DISTANCE tool on the left (tap the DISTANCE tool, then tap the segments to be measured) to show the lengths of the sides.[br][br] ([b]If you need to move your vertices, use the MOVE tool.)[/b][br][br] [b]-->[/b] In the space below, explain how your results confirm that this quadrilateral is a parallelogram. [br][b] (Write the theorem.)[/b]

3a) Move the vertices of this quadrilateral around to form a PARALLELOGRAM.

3b)

[b] -->[/b] In the applet above, use the ANGLE tool on the left (tap the ANGLE tool and then tap the interior of the polygon to measure all 4 angles at once) to show the angle measures. [br][br] [b] -->[/b] In the space below, explain how your results confirm that this quadrilateral is a parallelogram. [br][b](Reminder: this means to write the theorem.)[/b]

4a) Move the vertices of this quadrilateral around to form a PARALLELOGRAM.

4b)

[b] -->[/b] In the applet above, first use the SEGMENT tool to draw the two diagonals (tap the segment tool, tap A and then C, and repeat for the other diagonal ). [br][br] [b] -->[/b]Then use the MIDPOINT tool (tap the MIDPOINT tool and then tap the segment) to show the midpoint of the diagonals.[br][br] [b]-->[/b] In the space below, explain how your results confirm that this quadrilateral is a parallelogram. (Last reminder: this means to write the theorem.)

5a) Move the vertices of this quadrilateral around to form a RHOMBUS (that is NOT a square). (Hint: for example, if the slope of one side is 2/1, then the slope of a consecutive side can't be -1/2, but the slope CAN be -2/1.)

5b)

[b] -->[/b] In the applet above, use the SLOPE tool show the slopes of the sides, confirming that your quadrilateral is a parallelogram. *Reminder: if you made any sides vertical, Geogebra won't find the slope -- because there is no slope!*[br][br] [b] ( If you need to move your vertices, use the MOVE tool.)[/b][br][br] [b] -->[/b] Then use the SEGMENT tool to draw the diagonals.[br][br] [b] -->[/b] Then use the ANGLE tool (tap the ANGLE tool, and then tap each diagonal) to find the [b]angle formed by the diagonals.[/b][br][br] [b] -->[/b] In the space below, explain how your results confirm that your quadrilateral is a rhombus.

6a) Move the vertices of this quadrilateral around to form a RECTANGLE (that is NOT a square).

6b)

[b] -->[/b]In the applet above, use the SLOPE tool to confirm that your quadrilateral is a parallelogram.[br]*Reminder: if you made any sides vertical, Geogebra won't find the slope -- because there is no slope!*[br][br][b] -->[/b]Then use the ANGLE tool to find the measure of one angle of the parallelogram.[br][br][b] -->[/b]In the space below, explain how your results confirm that the quadrilateral is a rectangle.

7a) Move the vertices of this quadrilateral around to form a SQUARE.

7b)

[b] --> [/b]In the applet above, use the SLOPE tool to confirm that your quadrilateral is a parallelogram.[br][br][b] -->[/b] Then use the ANGLE tool to confirm that your parallelogram is a rectangle.[br][br][b] -->[/b] Then use the DISTANCE tool to find the length of two consecutive sides.[br][br] [b] -->[/b] Use the space below to explain how your results show that the quadrilateral is a square.