Question

place each statement in the correct category! statement is true no answer chosen statement is false no answers chosen possible answers: figures with 180° rotational symmetry have opposite sides that are congruent. to find the angle of rotational symmetry for an irregular polygon, divide 360 by the number of sides. the lines of reflective symmetry is equal to the number of sides of regular polygons. all regular polygons have reflective symmetry. all regular polygons have rotational symmetry. figures with no reflective symmetry have no rotational symmetry. the lines of reflective symmetry is equal to the number of sides of irregular polygons. all quadrilaterals have 90° rotation symmetry.

Explanation:

Step1: Analyze first statement

If a figure has 180 - degree rotational symmetry, when rotated 180 degrees it maps onto itself. This implies opposite sides are congruent. So, "Figures with 180° rotational symmetry have opposite sides that are congruent" is True.

Step2: Analyze second statement

The formula to find the angle of rotational symmetry of a regular polygon is $\frac{360^{\circ}}{n}$ (where $n$ is the number of sides). For irregular polygons, this formula doesn't apply as the shape is not uniform. So, "To find the angle of rotational symmetry for an irregular polygon, divide 360 by the number of sides" is False.

Step3: Analyze third statement

Regular polygons have as many lines of reflective symmetry as they have sides. For example, an equilateral - triangle has 3 sides and 3 lines of symmetry, a square has 4 sides and 4 lines of symmetry. So, "The lines of reflective symmetry is equal to the number of sides of regular polygons" is True.

Step4: Analyze fourth statement

By definition, all regular polygons have reflective symmetry. You can fold a regular polygon along certain lines and the two halves will match exactly. So, "All regular polygons have reflective symmetry" is True.

Step5: Analyze fifth statement

All regular polygons have rotational symmetry. A regular $n$-sided polygon has rotational symmetry of order $n$ (it can be rotated $\frac{360^{\circ}}{n}$ multiple times to map onto itself). So, "All regular polygons have rotational symmetry" is True.

Step6: Analyze sixth statement

There are figures like a non - symmetric parallelogram that has 180 - degree rotational symmetry but no reflective symmetry. So, "Figures with no reflective symmetry have no rotational symmetry" is False.

Step7: Analyze seventh statement

Irregular polygons do not necessarily have the number of lines of reflective symmetry equal to the number of sides. For example, a scalene triangle has 3 sides but 0 lines of symmetry. So, "The lines of reflective symmetry is equal to the number of sides of irregular polygons" is False.

Step8: Analyze eighth statement

Not all quadrilaterals have 90 - degree rotation symmetry. For example, a non - square rectangle has 180 - degree rotation symmetry but not 90 - degree rotation symmetry, and a trapezoid may have no rotational symmetry. So, "All quadrilaterals have 90° rotation symmetry" is False.

Answer:

Statement is True:

• Figures with 180° rotational symmetry have opposite sides that are congruent.
• The lines of reflective symmetry is equal to the number of sides of regular polygons.
• All regular polygons have reflective symmetry.
• All regular polygons have rotational symmetry.

Statement is False:

• To find the angle of rotational symmetry for an irregular polygon, divide 360 by the number of sides.
• Figures with no reflective symmetry have no rotational symmetry.
• The lines of reflective symmetry is equal to the number of sides of irregular polygons.
• All quadrilaterals have 90° rotation symmetry.