Explore the properties of rotation by following these steps.

✓ 1. Press Rotate to perform a rotation of △ABC about point P.

✓ 2. Make a conjecture:
What do you think is the measure of the angle of rotation? °

✓ 3. The diagram shows two corresponding vertices connected to the center of rotation. Use the protractor to measure it.
m∠APA' = °

✓ 4. The exact m∠APA' is 90°. How does this compare with the conjecture you made in step 2? They are equal. They are different.

✓ 5. Use the protractor to measure this angle: m∠BPB' = °

✓ 6. Use the protractor to measure this angle: m∠CPC' = °

✓ 7. The exact measure of each angle formed by connecting the center of rotation with corresponding vertices is 90°. What can you conclude about these angles? They all equal the angle of rotation. They are different.

✓ 8. Use the ruler to measure the length of these segments:
PA = units
PA' = units

✓ 9. Record the lengths of these segments:
PB = units
PB' = units

✓ 10. Record the length of these segments:
PC = units
PC' = units

✓ 11. The exact lengths of the segments connecting corresponding vertices with the center of rotation are:

PA  = 6.1 units   PA' = 6.1 units
PB  = 6.8 units   PB' = 6.8 units
PC  = 4.5 units   PC' = 4.5 units

Which segments have equal lengths:? no segments all segments corresponding segments