Ch 7 Extra Credit: Quadrilateral Creation
1. a). Move the vertices of this quadrilateral around to form a PARALLELOGRAM.
1b)
--> 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!* (If you need to move your vertices, use the MOVE tool.) --> In the space below, explain how your results confirm that this quadrilateral is a parallelogram by writing the appropriate theorem. (For example: One pair sides congruent and || --> parallelogram)
2a) Move the vertices of this quadrilateral around to form a PARALLELOGRAM.
2b)
--> 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. (If you need to move your vertices, use the MOVE tool.) --> In the space below, explain how your results confirm that this quadrilateral is a parallelogram. (Write the theorem.)
3a) Move the vertices of this quadrilateral around to form a PARALLELOGRAM.
3b)
--> 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. --> In the space below, explain how your results confirm that this quadrilateral is a parallelogram. (Reminder: this means to write the theorem.)
4a) Move the vertices of this quadrilateral around to form a PARALLELOGRAM.
4b)
--> 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 ). -->Then use the MIDPOINT tool (tap the MIDPOINT tool and then tap the segment) to show the midpoint of the diagonals. --> 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)
--> 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!* ( If you need to move your vertices, use the MOVE tool.) --> Then use the SEGMENT tool to draw the diagonals. --> Then use the ANGLE tool (tap the ANGLE tool, and then tap each diagonal) to find the angle formed by the diagonals. --> 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)
-->In the applet above, use the SLOPE tool to confirm that your quadrilateral is a parallelogram. *Reminder: if you made any sides vertical, Geogebra won't find the slope -- because there is no slope!* -->Then use the ANGLE tool to find the measure of one angle of the parallelogram. -->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)
--> In the applet above, use the SLOPE tool to confirm that your quadrilateral is a parallelogram. --> Then use the ANGLE tool to confirm that your parallelogram is a rectangle. --> Then use the DISTANCE tool to find the length of two consecutive sides. --> Use the space below to explain how your results show that the quadrilateral is a square.