Question

Tile X was used to create a seamless pattern when arranged as shown below. Which tile(s) from the options will create a seamless pattern (pattern without gaps)?

• A. A
• B. B
• C. C
• D. D

Hint:

For tessellation problems, always check for exact repetition of shapes. Even small differences in edges (straight vs curved, extra spikes, etc.) will prevent seamless patterns.

Answer 1

The Correct Option is A

Step 1: Observe the given tile X.
Tile X has an irregular polygonal shape with protrusions and indentations. These interlocking edges allow it to tessellate (form a repeating pattern without gaps).
Step 2: Check the given tessellation.
In the large shaded diagram, we see how multiple copies of tile X fit together perfectly, leaving no space in between. This means any correct option must match the same interlocking geometry of tile X.
Step 3: Compare each option with tile X.
(A) The shape in option A is identical to tile X. Its projections and indentations are the same, so it will tessellate seamlessly.
(B) Option B is different: its edges do not have the same “lock-and-key” structure. It would leave gaps.
(C) Option C is irregular with spiky edges, unsuitable for seamless tiling.
(D) Option D has curved edges unlike tile X, so it cannot fit into the given pattern.
Step 4: Conclude.
Only option A matches tile X and can create the same seamless pattern. Final Answer: \[ \boxed{\text{A}} \]