Question

question 2 of 10

only regular polygons with an odd number of sides can make a regular tessellation.

a. true
b. false

Explanation:

Analyze the definition of regular tessellations

A regular tessellation is a tiling of the plane using one type of regular polygon. For a regular polygon to tessellate the plane, the interior angle of the polygon must be an exact divisor of \(360^\circ\), so that a whole number of polygons can meet at a vertex without overlapping or leaving gaps.

Evaluate regular polygons that tessellate

The only regular polygons that can form a regular tessellation are:

1. Equilateral triangles (3 sides, interior angle \(60^\circ\), since \(6 \times 60^\circ = 360^\circ\))
2. Squares (4 sides, interior angle \(90^\circ\), since \(4 \times 90^\circ = 360^\circ\))
3. Regular hexagons (6 sides, interior angle \(120^\circ\), since \(3 \times 120^\circ = 360^\circ\))

Determine the truth value of the statement

The statement claims that "Only regular polygons with an odd number of sides can make a regular tessellation."
Since squares (4 sides) and regular hexagons (6 sides) both have an even number of sides and form regular tessellations, the statement is false.

Answer:

• A. True
• B. False (Correct answer)