Question

1. which regular polygon can completely tessellate a plane? a square a trapezoid an isosceles triangle a regular heptagon

Explanation:

A regular polygon can tessellate a plane if the interior angle of the polygon divides \(360^{\circ}\) evenly.

• For a square (a regular quadrilateral), the interior angle \(\theta=(4 - 2)\times180^{\circ}\div4 = 90^{\circ}\), and \(360\div90 = 4\).
• A trapezoid is not a regular polygon.
• An isosceles triangle is not a regular polygon (a regular triangle is equilateral).
• For a regular heptagon, the interior angle \(\theta=(7 - 2)\times180^{\circ}\div7=\frac{900^{\circ}}{7}\approx128.57^{\circ}\), and \(360\div\frac{900}{7}=\frac{360\times7}{900}=\frac{14}{5}\), which is not an integer.

Answer:

a square