Which of the following shapes can be used to tile (completely cover by repeating) a flat plane infinitely in all directions, without leaving gaps or overlaps?
Show Hint
- Circle
- Regular octagon
- Regular pentagon
- Rhombus
The Correct Option is D
Solution and Explanation
Step 1: Recall tiling rules.
To tile the plane perfectly, the shape's interior angles at a vertex must exactly sum to \(360^\circ\) when copies meet.
Step 2: Eliminate options.
- (A) Circle → cannot tile the plane, leaves gaps.
- (B) Regular octagon → does not tile by itself; needs squares to fill gaps.
- (C) Regular pentagon → cannot tile due to its \(108^\circ\) angle; multiples do not fit \(360^\circ\).
Step 3: Valid option.
(D) Rhombus → a parallelogram, and parallelograms always tessellate by repetition.
Final Answer:
\[
\boxed{\text{Rhombus}}
\]
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