What do you notice? What do you wonder?

Here is triangle .

1. Draw midpoint of side .

2. Rotate triangle using center to form a new triangle​​​​. Draw this triangle, and label the new point .

3. What kind of quadrilateral is ? Explain how you know.

The picture shows 3 triangles. Triangle 2 and Triangle 3 are images of Triangle 1 under rigid transformations.

1. Describe a rigid transformation that takes Triangle 1 to Triangle 2. What points in Triangle 2 correspond to points , , and in the original triangle?

2. Describe a rigid transformation that takes Triangle 1 to Triangle 3. What points in Triangle 3 correspond to points , , and in the original triangle?

3. Find two pairs of line segments in the diagram that are the same length, and explain how you know they are the same length.

4. Find two pairs of angles in the diagram that have the same measure, and explain how you know they have the same measure.

Here is isosceles triangle . Its sides and have equal lengths. Angle is . The length of is 5 units.

1. Reflect triangle across segment . Label the new vertex .

2. What is the measure of angle ?

3. What is the measure of angle ?

4. Reflect triangle across segment . Label the point that corresponds to as .

5. How long is segment ? How do you know?

6. What is the measure of angle ?

7. If you continue to reflect each new triangle this way to make a pattern, what will the pattern look like?