Math Problem Statement

Will this shape look exactly the same after a) a quarter turn? b) a half turn? c) a full turn?

Solution

Let's analyze the shape in your image and how it will look after a turn.

The shape appears to be a stylized figure, and we are considering three types of turns:

  1. Quarter turn – A quarter turn is 90 degrees. After a 90-degree rotation, the shape will not align with its original position, so it won't look exactly the same.
  2. Half turn – A half turn is 180 degrees. This would rotate the shape halfway around, but after this turn, the shape will look exactly the same as the original. This is because the shape is symmetrical along the central vertical axis.
  3. Full turn – A full turn is 360 degrees, meaning it completes a full rotation. The shape will also look exactly the same as the original after this full rotation.

From these, the correct answer is b) a half turn or c) a full turn.

Would you like more explanation on rotations or symmetry? Let me know if you need further details!

Additional questions:

  1. How would the shape look after a 270-degree turn?
  2. Can you describe the line of symmetry for this shape?
  3. How would this shape change if it was flipped vertically or horizontally?
  4. What types of shapes have rotational symmetry of order 2?
  5. How does a reflection differ from a rotation in terms of symmetry?

Tip:

For objects with symmetry, a rotation by a multiple of 180 degrees (half turn or full turn) will often result in the same shape. Keep an eye on lines of symmetry!

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Math Problem Analysis

Mathematical Concepts

Rotational Symmetry
Geometry

Formulas

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Theorems

Rotational Symmetry Theorem

Suitable Grade Level

Grades 4-6