Question

Ricky draws a square. He claims that any rotation about the center of the square that is a multiple of 30 degrees will carry the square onto itself. Which statement best describes Ricky’s claim?

a. Ricky’s claim is incorrect since not all rotations that carry a square onto itself are multiples of 30 degrees.
b. Ricky’s claim is incorrect since not all rotations that are multiples of 30 degrees carry a square onto itself.
c. Ricky’s claim is correct since any rotation that carries a square onto itself is a multiple of 30 degrees.
d. Ricky’s claim is correct since any rotation that is a multiple of 30 degrees carries a square onto itself.

Answer 1

Ricky's claim is incorrect since not all rotations that are multiples of 30 degrees carry a square onto itself.

Step-by-step explanation:

Ricky’s claim

The correct statement that describes Ricky’s claim is b. Ricky’s claim is incorrect since not all rotations that are multiples of 30 degrees carry a square onto itself.

While it is true that a rotation of 30 degrees about the center of a square will carry the square onto itself, there are other rotations, such as 60 degrees or 90 degrees, that also carry the square onto itself.

To see this, imagine rotating a square by 60 degrees. Each corner of the square will move to a new position that coincides with another corner of the square, resulting in the same square shape.

Therefore, rotations of multiples of 30 degrees are not the only rotations that carry a square onto itself.