Question

1. five polygons are shown.

select all the figures with rotational symmetry. (not including 0° or 360°)
□ image a: right, isosceles triangle
□ image b: rectangle
□ image c: square
□ image d: regular pentagon
□ image e: regular hexagon
select all the figures with 180° rotational symmetry. (3 answers)
□ image a: right, isosceles triangle
□ image b: rectangle
□ image c: square
□ image d: regular pentagon
□ image e: regular hexagon
select all the figures with reflectional symmetry.
□ image a: right, isosceles triangle
□ image b: rectangle
□ image c: square
□ image d: regular pentagon
□ image e: regular hexagon

Explanation:

Step1: Recall symmetry rules

Rotational symmetry of 180°: figure looks same after 180 - degree turn. Reflectional symmetry: has a line of symmetry.

Step2: Analyze each polygon

• Polygon A: no 180 - degree rotational symmetry, has 1 line of reflectional symmetry.
• Polygon B: has 180 - degree rotational symmetry, has 2 lines of reflectional symmetry.
• Polygon C: has 180 - degree rotational symmetry, has 4 lines of reflectional symmetry.
• Polygon D: no 180 - degree rotational symmetry, has 5 lines of reflectional symmetry.
• Polygon E: has 180 - degree rotational symmetry, has 6 lines of reflectional symmetry.

Answer:

• Figures with 180° rotational symmetry: B. rectangle, C. square, E. regular hexagon
• Figures with rotational symmetry (not 0° or 360°): B. rectangle, C. square, E. regular hexagon
• Figures with reflectional symmetry: A. right, isosceles triangle, B. rectangle, C. square, D. regular pentagon, E. regular hexagon