Question

A polygon is a square only if it has four right angles. Express this statement in if-then form.

A) If a polygon has four right angles, then it is a square.
B) If a polygon is a square, then it has four right angles.
C) All polygons with four right angles are squares.
D) Squares are polygons with four right angles.

Answer 1

The statement 'A polygon is a square only if it has four right angles' is best represented in if-then form as 'If a polygon is a square, then it has four right angles', corresponding to option B is correct.

Step-by-step explanation:

The statement 'A polygon is a square only if it has four right angles' can be expressed in if-then form as: If a polygon is a square, then it has four right angles.

This corresponds to option B. It is important to note that having four right angles is a necessary condition for a polygon to be a square, but on its own, it is not always sufficient since there are other requirements for a polygon to be classified as a square, such as having all sides of equal length.

Option A is incorrect because a polygon can have four right angles and not be a square; for example, a rectangle also has four right angles but is not a square unless all sides are equal. Option C overgeneralizes by implying all polygons with four right angles are squares, which is false. Option D describes a property of squares but does not use the if-then structure.

This means that all squares must have four right angles, although the presence of four right angles alone does not guarantee the polygon is a square.