DIRECTIONS: Follow the instructions to draw a quadrilateral. Take any important measures (the first one is done for you) that will help you to determine the best name for it. Don’t be satisfied with your answer until you pull and tug on the vertices to make sure that it doesn’t change shapes.

1. Draw a segment. Select the segment with your arrow tool.

Ø Using the Construct menu, select point at midpoint.

Ø Now, in order, (hold the shift key down to be able to choose more than one point if you are using version 3) choose the midpoint of the segment and one of the end points of the segment. On the Construct menu choose Circle by Center and Point.

Ø Select the diameter and the center and select (on the Construct menu) perpendicular line.

Ø Select the new perpendicular line and the circle and choose (on the Construct menu) Point at Intersection.

Ø Select the two points that you just created (at the ends of the new diameter) and on the Construct menu, choose Segment.

Ø Select the line (outside the circle) and from the Display menu, choose Hide Line. Select the circle and from the Display menu, choose Hide Circle. Now you have the diagonals of the mystery quadrilateral. What are three properties of the diagonals that you have constructed?

1. ______________________________

2. ______________________________

3. ______________________________

Ø Now, complete the quadrilateral. Select all four of the endpoints of the segments. On the Construct menu choose Segment.

Ø To label your points, choose the Text tool and click on each of the endpoints of the segments. It doesn’t matter what labels are chosen by the computer. If you want or need to move the labels, select the arrow tool and drag the label to a more appropriate place.

It’s time to investigate...

Ø Select each of the four sides of the quadrilateral and from the Measure Menu, choose Length. (If these are put in a place that is not convenient, select the arrow tool and move them to a more appropriate place.)

Ø To measure the angles of this quadrilateral, use the arrow tool and shift key to select the three points of an angle (vertex must be the second point selected) and then from the Measure Menu, choose Angle. Repeat this till all of the angle measures are displayed.

Drag and tug on each of the vertices. What is the name of this quadrilateral?__________________

How do you know?

2. Draw a segment. Select the segment with your arrow tool.

Ø Using the Construct menu, select point at midpoint.

Ø Now, in order, hold the shift key down (to be able to choose more than one point) choose the midpoint of the segment and one of the end points of the segment. On the Construct menu choose Circle by Center and Point.

Ø Select the diameter and the center and select (on the Construct menu) perpendicular line.

Ø Use the point tool and select a point on the perpendicular line either on the interior or exterior of the circle. Select (in order) the center of the circle and your new point and on the Construct menu, choose circle.

Ø Select the new circle and the line and from the Construct menu, choose Point at Intersection.

Ø Select the two points that you just created (at the ends of the diameter of the new circle) and on the Construct menu, choose Segment.

Ø Select the line (outside the circle) and from the Display menu, choose Hide Line. Select the circles and from the Display menu, choose Hide Circle. Now you have the diagonals of the mystery quadrilateral. What are three properties of the diagonals that you have constructed?

1. ______________________________

2. ______________________________

3. ______________________________

Ø Now, complete the quadrilateral. Select all four of the endpoints of the segments. On the Construct menu choose Segment.

Ø Label your points.

It’s time to investigate...

Ø Measure the lengths of all four sides of the quadrilateral.

Ø Measure the angles of this quadrilateral.

Drag and tug on each of the vertices. What is the name of this quadrilateral?__________________

How do you know?

3. Draw a segment. Select the segment with your arrow tool.

Ø Using the Construct menu, select point at midpoint.

Ø Now, in order, hold the shift key down (to be able to choose more than one point) choose the midpoint of the segment and one of the end points of the segment. On the Construct menu choose Circle by Center and Point.

Ø Using the point tool choose another point on the circle.

Ø Select the new point and the center. Change the segment tool to the line tool (hold down the mouse on the segment and choose the line from the horizontal menu) and select (on the Construct menu) line . If segment is your only choice on the Construct menu, you need to make sure that you’ve chosen the line tool first - not the segment.

Ø Select the circle and the line and on the Construct menu, choose Points at Intersection,

Ø Select the two points on the line that you just created (at the ends of the diameter of the circle) and on the Construct menu, choose Segment. (Again, make sure that you’ve chosen the segment tool from the tool menu.)

Ø Select the line (outside the circle) and from the Display menu, choose Hide Line. Select the circle and from the Display menu, choose Hide Circle. Now you have the diagonals of the mystery quadrilateral. What are two properties of the diagonals that you have constructed?

1. ______________________________

2. ______________________________

Ø Now, complete the quadrilateral. Select all four of the endpoints of the segments. On the Construct menu choose Segment.

Ø Label your points.

It’s time to investigate...

Ø Measure the lengths of all four sides of the quadrilateral.

Ø Measure the angles of this quadrilateral.

Ø It might also be helpful to measure the angles where the diagonals intersect.

Drag and tug on each of the vertices. What is the name of this quadrilateral?__________________

How do you know?

4. Draw a segment. Select the segment with your arrow tool.

Ø Using the Construct menu, select point at midpoint.

Ø Now, in order, hold the shift key down (to be able to choose more than one point) choose the midpoint of the segment and one of the end points of the segment. On the Construct menu choose Circle by Center and Point.

Ø Using the point tool, select another point on the circle.

Ø Select the new point and the center of the circle. Using the line tool, draw a line.

Ø Use the point tool and select a point on the new line either on the interior or exterior of the circle. Select (in order) the center of the circle and your new point and on the Construct menu, choose circle.

Ø Select the new circle and the line and from the Construct menu, choose Point at Intersection.

Ø Select the two points that you just created (at the ends of the diameter of the new circle) and on the Construct menu, choose Segment.

Ø Select the line (outside the circle) and from the Display menu, choose Hide Line. Select the circles and from the Display menu, choose Hide Circle. Hide the extra point on one of the diagonals (not the endpoints or center of the circle). Now you have the diagonals of the mystery quadrilateral. What are two properties of the diagonals that you have constructed?

1. ______________________________

2. ______________________________

Ø Now, complete the quadrilateral. Select all four of the endpoints of the segments. On the Construct menu choose Segment.

Ø Label your points.

It’s time to investigate...

Ø Measure the lengths of all four sides of the quadrilateral.

Ø Measure the angles of this quadrilateral.

Ø It might also be helpful to measure the angles where the diagonals intersect.

Drag and tug on each of the vertices. What is the name of this quadrilateral?__________________

How do you know?

5. Making a quadrilateral following a Geometers Sketchpad script.

Given: (choose two points A and B)

Point A

Point B

---------------

Steps:

1. Let [j] = Segment between Point A and Point B. (Draw a segment between A and B)

2. Let [C] = Random point on Segment [j]. (Select the segment and on the constuct menu, choose Point on Object)

3. Let [k] = Perpendicular to Segment [j] through Point [C]. (Select the segment and the point that was just made and from the Construct menu, choose perpendicular line)

4. Let [D] = Random point on Line [k]. (Select the perpendicular line and on the construct menu, choose Point on Object.)

5. Let [c1] = Circle with center at Point [C] passing through Point [D]. (Select the point(C) on segment AB and the random point D from step 4. On the Construct menu, choose Circle by Center and Point.)

(Steps 6 and 7 are identifying the intersection points of the circle and the perpendicular segment.)

6. Let [E] = Intersection of Circle [c1] and Line [k].

7. Let [F] = Intersection of Circle [c1] and Line [k].

8. Let [l] = Segment between Point [E] and Point [F]. (Select points E and F and from the Construct menu, choose Segment.)

Hide the line and Hide your circle.

(Steps 9-12 draw the segments that form the quadrilateral. Choose the vertices in order, and from the Construct menu, choose Segment.)

9. Let [m] = Segment between Point [A] and Point [E].

10. Let [n] = Segment between Point [E] and Point [B].

11. Let [o] = Segment between Point [B] and Point [F].

12. Let [p] = Segment between Point [F] and Point A.

It’s time to investigate...

Measure the sides of the quadrilaterals.

13. Let Measurement [m1] = Distance(A to [E]).

14. Let Measurement [m2] = Distance([E] to B).

15. Let Measurement [m3] = Distance(B to [F]).

16. Let Measurement [m4] = Distance([F] to A).

Measure the angles.

17. Let Measurement [m5] = Angle(A-[E]-B).

18. Let Measurement [m6] = Angle([E]-B-[F]).

19. Let Measurement [m7] = Angle(B-[F]-A).

20. Let Measurement [m8] = Angle([F]-A-[E]).

Drag and tug on each of the vertices. What is the name of this quadrilateral?__________________

How do you know?