This activity gives students an opportunity to determine and request the information needed to define a rotation.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

Students may need to be reminded of the tools in their geometry toolkits, such as tracing paper, straightedges, and compasses.

Students may try to estimate the measure of the angle of rotation. Remind them they can name an angle with 3 letters.

After students have completed their work, share the correct answers, and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “What kinds of questions were the most useful to ask?” (What is the center of rotation? What is the angle of rotation?)
• “What information do you need to completely describe a rotation?” (The center, the direction, and the angle.)

Highlight for students that it is possible to precisely describe a rotation without giving an angle measure in degrees.

The goal of this activity is to practice applying the definition of rotation. In this activity, students rotate a segment around its endpoint to create an isosceles triangle. By rotating a segment around one endpoint, students can observe that the distance between the center of rotation and a point is the same as the distance between the center of rotation and the image of that point. This observation is later captured in the formal definition of rotation.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

Display a right isosceles triangle with base  and an equilateral triangle . Invite students to share what they know is true and what they conjecture might be true.

Here are some conjectures and observations students may discuss: 

• Rotations preserve the distance to the center of rotation.
• The angle bisector of angle is also the perpendicular bisector of the base () of an isosceles triangle.
• The two base angles (angle and angle ) of an isosceles triangle are congruent.
• An isosceles triangle where angle is 60 degrees is also equilateral.
• Any fact that is true about an isosceles triangle is also true about an equilateral triangle.

It is not necessary at this time to formalize the language of these ideas. This will come later as students prove some of these statements in a subsequent unit.

Students may not notice any properties other than that rotation preserves distances to the center of rotation. Encourage these students to use tracing paper to make other conjectures about side lengths or angles.