Only regular polygons with an even number of sides are symmetrical.A.TrueB.FalseSUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify what symmetrical polygons are.
2. Explore the properties of regular polygons and their symmetry based on the number of sides.

Relevant Concepts

1. Regular Polygon Definition: A regular polygon is defined as a polygon with all sides and all angles equal.
2. Symmetry in Polygons: A polygon is symmetrical if it can be divided into two identical halves that are mirror images of each other.

Analysis and Detail

1. Even-Sided Polygons: Regular polygons with an even number of sides (e.g., square, hexagon) can be divided into two equal halves through lines of symmetry that run through opposite vertices or the midpoints of opposite sides.
2. Odd-Sided Polygons: Regular polygons with an odd number of sides (e.g., triangle, pentagon) can also exhibit symmetry, particularly through lines that pass through a vertex and the midpoint of the opposite side.

Verify and Summarize

Both even and odd-sided regular polygons can have symmetry. Therefore, the assertion that only regular polygons with an even number of sides are symmetrical is inaccurate.

Final Answer

B. False - Regular polygons with an odd number of sides can also be symmetrical.