Question

which of the following can tessellate by itself?
a. equilateral triangle
b. semi - circle
c. ellipse
d. circle

Explanation:

Step1: Recall tessellation condition

A shape can tessellate if the sum of angles at a vertex is \(360^{\circ}\).

Step2: Analyze each option

• Equilateral triangle: Each interior angle is \(60^{\circ}\). \(6\times60^{\circ} = 360^{\circ}\), so it can tessellate.
• Semi - circle: The angle at the straight edge is \(180^{\circ}\), but it has a curved edge. Curved edges don't fit together without gaps for tessellation.
• Ellipse: It has a curved shape. Curved shapes (non - circular with varying curvature in this case) can't tessellate without gaps.
• Circle: It has a curved shape. When placed together, there are gaps between circles.

Answer:

A. Equilateral triangle