Question
Milo has an end table with a top surface in the shape of a regular octagon. He is moving the table to clean the floor around the table's legs with the vacuum cleaner.
Which of these statements are correct? Select all that apply.
A.
Rotations of the table will not affect the side lengths but will affect the angle measures.
B.
Interior angle measure sums may be affected by a rotation of the table top.
C.
Parallel lines found on the table top will remain parallel after any rigid motion.
D.
Rotations of the table will not affect the angle measures of the top surface.
E.
Translations of the table will not affect the angle measures of the top surface.
Which of these statements are correct? Select all that apply.
A.
Rotations of the table will not affect the side lengths but will affect the angle measures.
B.
Interior angle measure sums may be affected by a rotation of the table top.
C.
Parallel lines found on the table top will remain parallel after any rigid motion.
D.
Rotations of the table will not affect the angle measures of the top surface.
E.
Translations of the table will not affect the angle measures of the top surface.
Answers
GPT-4o mini
To analyze the statements regarding Milo's octagonal table, let's evaluate each one based on the properties of geometric figures, especially concerning transformations such as rotations and translations.
A. **Rotations of the table will not affect the side lengths but will affect the angle measures.**
- **Incorrect.** Rotations will not affect either the side lengths or the angle measures of the octagon; they remain unchanged.
B. **Interior angle measure sums may be affected by a rotation of the table top.**
- **Incorrect.** The sum of interior angles in any polygon is a property based on the number of sides and is not affected by rotation. For a regular octagon, the sum of the interior angles is always the same.
C. **Parallel lines found on the table top will remain parallel after any rigid motion.**
- **Correct.** Rigid motions (like rotations or translations) do not affect relationships between lines, including parallelism.
D. **Rotations of the table will not affect the angle measures of the top surface.**
- **Correct.** Rotating the table does not change the measures of the angles; the angle measures remain constant.
E. **Translations of the table will not affect the angle measures of the top surface.**
- **Correct.** Similar to rotations, translations do not alter the angle measures or any intrinsic properties of the octagon.
### Summary of Correct Statements:
- C.
- D.
- E.
Therefore, the correct answers are C, D, and E.
A. **Rotations of the table will not affect the side lengths but will affect the angle measures.**
- **Incorrect.** Rotations will not affect either the side lengths or the angle measures of the octagon; they remain unchanged.
B. **Interior angle measure sums may be affected by a rotation of the table top.**
- **Incorrect.** The sum of interior angles in any polygon is a property based on the number of sides and is not affected by rotation. For a regular octagon, the sum of the interior angles is always the same.
C. **Parallel lines found on the table top will remain parallel after any rigid motion.**
- **Correct.** Rigid motions (like rotations or translations) do not affect relationships between lines, including parallelism.
D. **Rotations of the table will not affect the angle measures of the top surface.**
- **Correct.** Rotating the table does not change the measures of the angles; the angle measures remain constant.
E. **Translations of the table will not affect the angle measures of the top surface.**
- **Correct.** Similar to rotations, translations do not alter the angle measures or any intrinsic properties of the octagon.
### Summary of Correct Statements:
- C.
- D.
- E.
Therefore, the correct answers are C, D, and E.