1. Plot three points on the coordinate plane and label them A, B, and C. (Be sure that all three points do not lie in a straight line.) Now join the points two at a time using straight paths. How many unique straight paths can you make through the points? Which geometric figure is formed?

2. The three paths intersect in pairs at the points A, B, and C. Measure and record the angle formed at each intersection. Also measure and record the lengths of the straight paths, or sides. Capture the image, and paste or insert it in the space below.

3. The three straight paths, AB, BC, and AC, meet each other at three points, A, B, and C. How do these points of intersection differ from each other? Explain the differences in terms of the angles that you see. Also look at the length of the side opposite each angle. What pattern do you see regarding the measurements? In what situation would all the points of intersection resemble one another?

4. Use GeoGebra to move points A, B, and C to the locations shown by the ordered pairs in the table. Record the length of each side and the measure of each angle for the resulting triangle. Note that the length of a line segment is denoted with two letters but no bar on top. For example, AB is read as "the length of AB."

Location	AB	BC	AC	mABC	mBAC	mACB
A(3, 4), B(1, 1), C(5, 1)
A(4, 5), B(2, 1), C(7, 3)
A(3, 6), B(3, -2), C(-3, -2)

5. If you move point C toward point B along BChow does mABCchange? How do mBACand mACBchange? What happens to these angles if you move point C away from point B alongBC?

6. Delete ACand focus on the intersection of ABand BC. Keeping points B and C fixed, move point A to different locations and observe how ABCchanges. What must you do to increase or decrease mABC? What happens if you move point A to a location directly on CB? What is mABCat this location? Explain.