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Chapter 10: Problem 54

Explain why a square is a regular polygon, but a rhombus is not.

Short Answer

Expert verified
A square is a regular polygon since it has all sides of equal length and all angles of 90 degrees. On the other hand, a rhombus is not a regular polygon because while it has all sides of equal length, its angles are not of equal measure.

Step by step solution

01

Define a regular polygon

By definition, a regular polygon is a polygon that has all sides of equal length and all angles of equal measure.
02

Define a square

A square is a type of quadrilateral that has all sides of the same length. Moreover, all angles of a square are 90 degrees, which means they are all equal to each other.
03

Define a rhombus

A rhombus is another type of polygon which also has all four sides of equal length. However, the angles in a rhombus are not necessarily equal. For example, in a rhombus, opposite angles are equal but adjacent angles are supplementary (they add up to 180 degrees), and are not necessarily of equal measure.
04

Compare the definitions

Comparing the definitions, it is apparent that a square satisfies all the conditions for being a regular polygon - equal sides and equal angles. However, a rhombus, while having equal sides does not have equal angles. Thus, it does not fulfill all the criteria to be labeled as a regular polygon.

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