# Investigation of the Triangle

This activity will help to connect many of the different ideas you have learned about triangles and geometry. You will learn about angle sum, angle properties, classification of triangles, and collinearity. You will use the task sheet to guide you as you work with the applet.

*Move the slider back and forth, and observe what happens to the triangle, side lengths, angles, and angle sum.*1. As you increase the size of α, what happens to the side lengths? Which sides increase, decrease, or stay the same? Why does this occur? 2. As you decrease the size of α, what happens to the side lengths? Which sides increase, decrease, or stay the same? Why does this occur? 3. What happens to the other two angles as α increases? As α decreases? 4. What is always true of the other two angles? What is always true of side lengths a and a’? How can we classify this type of triangle? 5. What happens to the angle sum as α increases? As α decreases? Why does this occur?

*Click the box that says show parallel line. Now we will again explore using the slider tool.*6. Move the slider all the way to the right. What happens to the size of the angles? What happens to the side lengths? Is this shape still a triangle? Explain why or why not. 7. Move the slider all the way to the left. What happens to the size of the angles? What happens to the side lengths? Is this shape still a triangle? Explain why or why not. 8. What happens to points A, A’, and B when α is 0 degrees or 180 degrees? Use the parallel line to help you answer this question.

*Definition: Two points are said to be collinear if they lie on a single straight line.*9. When are points A, A’, and B collinear? 10. What do you think would happen if we answered questions 1-9 using an equilateral triangle? With a scalene triangle? 11. Using the slider, create an acute triangle. Sketch it on your paper and label the angle sizes. Explain why it is acute. Repeat this process for both right and obtuse triangles.