W. Gary Martin home page > CTSE 7970 > Lab 4
CTSE
7970, Summer 2001
Lab 4 — Geometry’s Sketchpad
Before starting the lab: Open Geometer’s Sketchpad. Then go under the Display menu and choose Preferences. Click on the box labeled “Points” under Auto Show Labels so that an X shows. Then click OK.
1. Making a triangle.
a. Select the "point" icon on the toolbar. Click in the screen three times to make three points.
b. Select the "segment" icon on the toolbar. Point at one of the points. Click and drag to connect the segment to one of the other points. Then connect the other two pairs of points to form a triangle. Your picture should look something like this:
c. Select the "pointer" icon on the toolbar. Click and drag the points to form different kinds of triangles.
2. Exploring different types of triangles.
a. Now select the "circle" icon on the toolbar. Draw a circle from one of the vertices going through another vertex by pointing at a vertex, then clicking and dragging the pointer to point to the second vertex.
b. Draw a circle through each pair of points. Your picture should look something like this:
c. Select the "pointer" icon and drag the points around to form various kinds of triangles. What happens when the triangle is isosceles? Regular? Make various interesting observations. (You may want to select the sides the triangle, and select the heavy “Line weight” under the “Display” menu.)
3. Constructing different types of triangles.
a. Use what you learned in #2 to construct a triangle that is ALWAYS regular. That is, when you drag a vertex to a new location the triangle should still be regular.
b. Now construct an isosceles triangle!
4. Measuring lengths.
a. Open a new sketch. Draw a segment (as in AB below). Then draw a circle with a center at one of its endpoints (B in the example below) but that does NOT go through the other endpoint. Now draw another point on the circle (D below); connect that to each endpoint of the segment to form a triangle (ADB in the picture below). Your picture should look something like this:
b. Click and move the vertex on the circle (point D above). What do you notice? Click and move other objects.
c. Click on the "pointer" icon. Then click on one of the sides. Select "Length" from the Measure menu. Measure the sides of the other sides. Click and move the vertex on the circle (point D) above. What happens?
d. Now click on one of the lengths, hold down the shift key, and then click on the other two lengths. Under the Measure menu, choose “Calculator”. Use the calculator to computer the perimeter of the triangle. What is the greatest perimeter possible? What is the shortest possible perimeter?
5. Measuring angles.
a. Open a new sketch. Now select the "line" tool by pointing to the "segment" tool and holding down; pull across until the line icon shows. Then draw a line. Use one of the points on that line as part of a second line, then use one of the points on the second line to draw a third line. Your picture should look something like this:
b. Now measure an angle by doing the following. Select the "pointer" icon. Click on the point along one of the rays of the angle. WHILE HOLDING THE SHIFT KEY, click on the vertex of the angle, then on the third point. Three points determining the angle should be highlighted. Choose Angle from the Measure menu.
c. Measure the other angle between the two lines.
d. Now adjust the two lines so they are parallel. Make one or more observations.
e. Use the "point" icon to add a point on line BD above CD and a point below AB; measure these angles.
6. Open a new sketch. Draw a quadrilateral using the "segment" tool. Measure each angle of the quadrilateral. Move the vertices and observe what happens to the angles. Make your quadrilateral into a parallelogram. What happens to its angles?
7. Measuring area and perimeter.
a. Open a new sketch. Draw a triangle. Then shift-click so that all three vertices are highlighted. From the Construct menu, select Polygon Interior. Your sketch should look something like:
b. Click on the shaded area. Then under Measure, choose Perimeter. Then choose Area.
c. Write down the area and perimeter of your triangle. Then move ONLY ONE of the vertices so that the triangle has the SAME area as before. Write down its perimeter. Repeat this several times. What do you notice about the different locations of the point that you move?
8. Perpendicular lines.
a. Open a new sketch. Draw a line and a point not on the line. Shift-click so that both the point and point are highlighted. Then select Perpendicular Line under the Construct menu.
b. Now construct a perpendicular line through the point perpendicular to the second line. Your sketch should look something like this:
c. What do you notice? Move the points around and see if your observation still works! Can you explain why?
9. A (possible) surprise.
a. Open a new sketch. Draw a triangle. Then select one of the sides of the triangle and select Midpoint under the Construct menu. Now construct the perpendicular to that same side, going through the midpoint.
b. Do the same for each of the other points.
c. What do you notice? Move the points around and see what happens!
d. Select two of the lines and choose Intersection from the Construct menu. Then draw an interesting circle. Can you explain what happened?
10. Construct a rectangle; it should remain a rectangle even when you drag its vertices! (HINT: #8 gives you a good start on this!)
11. Use the commands under Construct to make a parallelogram; it should remain a parallelogram even when you drag its vertices! (HINT: Draw two of the sides, then use the Parallel Line construction to make the other two lines.) Use the measure tool to make various interesting observations!
12. Draw other geometric shapes so that they remain that shape when its vertices are dragged around. Explore various of its properties:
a. Square
b. Rhombus
c. Trapezoid
d. Isosceles trapezoid
e. Regular octagon
f. Regular hexagon
13. Draw a triangle, then construct a circle inscribed in that triangle. (HINT: There is a command under “Constructions” that is particularly helpful.)
14. Open a new sketch. Draw a triangle. You will use this “given triangle” for the remaining parts of this section.
15. Congruent triangles.
a. Draw a line that does not touch the given triangle. Shift click on a point on the line and one side of the triangle. Under Construct, select “Circle by radius+center”. Then click on one of the points of intersection of the circle and line.
b. Make two more judicious constructions of circles by radius and center in order to form a second triangle that remains congruent to the first.
16. Develop a different method to draw a triangle congruent to the first triangle.
17. Draw a triangle whose sides are double that of the first triangle.