Question

drag each shape to the correct bucket to tell what type of symmetry, if any, the shape has.
keyboard help
line symmetry only rotational symmetry only both line and rotational symmetry no symmetry

Explanation:

Step1: Recall the definitions

• Line symmetry: A shape has line symmetry if there is a line (axis of symmetry) such that one side of the line is the mirror - image of the other side.
• Rotational symmetry: A shape has rotational symmetry if it looks the same after a rotation (less than \(360^{\circ}\)) about its center.

Step2: Analyze each shape

• Square:
• Line symmetry: A square has 4 lines of symmetry (two diagonals and two lines joining the mid - points of opposite sides).
• Rotational symmetry: A square looks the same when rotated by \(90^{\circ},180^{\circ},270^{\circ}\). So, it has both line and rotational symmetry.
• Regular hexagon:
• Line symmetry: A regular hexagon has 6 lines of symmetry (3 lines joining opposite vertices and 3 lines joining the mid - points of opposite sides).
• Rotational symmetry: A regular hexagon looks the same when rotated by \(60^{\circ},120^{\circ},180^{\circ},240^{\circ},300^{\circ}\). So, it has both line and rotational symmetry.
• Isosceles trapezoid:
• Line symmetry: An isosceles trapezoid has 1 line of symmetry (the line passing through the mid - points of the non - parallel sides).
• Rotational symmetry: If we rotate an isosceles trapezoid by any angle other than \(360^{\circ}\), it does not look the same. So, it has line symmetry only.
• Scalene triangle:
• Line symmetry: A scalene triangle has no line of symmetry (since all sides and angles are of different measures).
• Rotational symmetry: If we rotate a scalene triangle by any angle other than \(360^{\circ}\), it does not look the same. So, it has no symmetry.

Answer:

• Square: Both Line and Rotational Symmetry
• Regular hexagon: Both Line and Rotational Symmetry
• Isosceles trapezoid: Line Symmetry Only
• Scalene triangle: No Symmetry