Math 487 Lab #1, October 2, 2002

In this lab we will compare and contrast the construction of geometrical figures with physical drawing tools and with Sketchpad.

Part 1. Introduction to Construction with Straightedge and Compass (physical tools on paper)

• Mark two points A and B on a sheet of paper. Use your compass to draw a circle with center A through B. Mark a point C on the circle and use a straightedge to draw the 3 edge segments of triangle ABC. What kind of triangle is this? Why?
• Mark two points A and B on paper. Use your compass to draw a circle with center A through B. Then use your compass to draw a circle with center B through A. Let C be a point of intersection of the two circles. What kind of triangle is ABC? Why?
• Let D be the second point of intersection of the two circles. What kind of figure is ADBC? Construct the line CD. How is it related to segment AB? If M is the intersection of line CD and segment AB, what special point is M on each of these segments?
• Draw two rays with common vertex A. Use your compass to mark off points B and C on each of the rays so that ABC is isosceles. Now use your compass to draw intersecting circles of equal radius, one with center B and one with center C. Let D be one of the points of intersection of the two circles. What kind of figure is ABDC? How is line AD related to angle BAC?

Part 2. Introduction to Construction with Sketchpad Toolbar

• Open the Sketchpad program by clicking on the GSP icon. The toolbar is on the left. One tool is a line or segment tool (straightedge) and one is a circle tool (compass).
• Experiment with the tools following the instructions given in the lab.
• Repeat the constructions from Part 1 with Sketchpad. See that the figures (e.g., the equilateral triangle and perpendicular bisector) pass the Drag Test. (This will be explained.)

Part 3. Introduction to Sketchpad Menus

• Draw a segment AB. With the Construct menu construct the midpoint M of AB and also the line m through M that is perpendicular to AB. Construct a point C on m. Construct the segments AC and BC. Measure the lengths of the segments; drag C and see how the measurements change. Measure the size of the angles; drag the figure again and observe the measurements.
• Construct a second point D on m and construct the segments AD and BD. Construct the interior of the quadrilateral ACBD.

Part 4. Constructing a Square and Copying a Triangle

• Construct a Square that will pass the "Drag Test."
• Draw a triangle ABC in a new Sketch and also a point D. Construct E and F so that Triangle ABC is congruent to DEF.