Here is triangle .

1. Rotate triangle around the midpoint of side . Label the new vertex .

2. Rotate triangle around the midpoint of side . Label the new vertex .

3. Look at angles , , and . Without measuring, write what you think is the sum of the measures of these angles. Explain or show your reasoning.

4. Is the measure of angle equal to the measure of any angle in triangle ? If so, which one? Explain your reasoning.

5. Is the measure of angle equal to the measure of any angle in triangle ? If so, which one? Explain your reasoning.

6. What is the sum of the measures of angles , , and ? Explain your reasoning.

Here is triangle . Line is parallel to line .

Point B lies on line D E. Triangle B A C is drawn. Angle A B C is labeled b degrees. Angle B A C is labeled a degrees. Angle A C B is labelled c degrees.

1. What is the sum of the measures of angle , angle , and angle ?

2. Use your answer to explain why .

3. Explain why your argument will work for any triangle: that is, explain why the sum of the angle measures in any triangle is .

This diagram shows a square that has been made by images of triangle under rigid transformations.

Quadrilateral B D F H. Angles B, D, F, and H are marked as right angles. Point C lies on B D. Point E lies on D F. Point G lies on F H. Point A lies on B H. Segments A C, C E, E G, and G A are drawn.

Given that angle measures , find as many other angle measures as you can.