Question

rotational and reflectional symmetry

1. draw all lines of symmetry
2. state the order of rotation - # of times it rotates into itself before it first turns 360
3. state the angle of rotation

order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry
order of rotation
angle of rotation
lines of symmetry

Explanation:

Step1: Recall line - symmetry concept

A line of symmetry divides a shape into two congruent parts.

Step2: Recall rotation - symmetry concepts

The order of rotation is the number of times a shape fits onto itself during a 360 - degree rotation. The angle of rotation $\theta=\frac{360^{\circ}}{\text{Order of rotation}}$.

For the rectangle (top - left):

• Lines of symmetry: A rectangle has 2 lines of symmetry (vertical and horizontal).
• Order of rotation: 2 (it fits onto itself 2 times in a 360 - degree rotation).
• Angle of rotation: $\frac{360^{\circ}}{2}=180^{\circ}$

For the isosceles triangle (top - middle):

• Lines of symmetry: 1 (the line that bisects the angle between the equal sides).
• Order of rotation: 1 (it only fits onto itself once in a 360 - degree rotation).
• Angle of rotation: $360^{\circ}$

For the parallelogram (top - right):

• Lines of symmetry: 0
• Order of rotation: 2
• Angle of rotation: $180^{\circ}$

For the square - like shape (second row, left):

• Lines of symmetry: 4 (2 diagonals and 2 perpendicular bisectors of the sides).
• Order of rotation: 4
• Angle of rotation: $\frac{360^{\circ}}{4}=90^{\circ}$

For the irregular shape (second row, middle):

• Lines of symmetry: 0
• Order of rotation: 1
• Angle of rotation: $360^{\circ}$

For the regular pentagon (second row, right):

• Lines of symmetry: 5
• Order of rotation: 5
• Angle of rotation: $\frac{360^{\circ}}{5}=72^{\circ}$

For the curved - shape (third row, left):

• Lines of symmetry: 1
• Order of rotation: 1
• Angle of rotation: $360^{\circ}$

For the arrow - like shape (third row, middle):

• Lines of symmetry: 1
• Order of rotation: 1
• Angle of rotation: $360^{\circ}$

For the ellipse (third row, right):

• Lines of symmetry: 2 (major and minor axes).
• Order of rotation: 2
• Angle of rotation: $180^{\circ}$

For the star - like shape (fourth row, left):

• Lines of symmetry: 4
• Order of rotation: 4
• Angle of rotation: $90^{\circ}$

For the regular hexagon (fourth row, middle):

• Lines of symmetry: 6
• Order of rotation: 6
• Angle of rotation: $\frac{360^{\circ}}{6}=60^{\circ}$

For the 5 - pointed star (fourth row, right):

• Lines of symmetry: 5
• Order of rotation: 5
• Angle of rotation: $72^{\circ}$

Answer:

Shape	Lines of Symmetry	Order of Rotation	Angle of Rotation
Isosceles Triangle	1	1	$360^{\circ}$
Parallelogram	0	2	$180^{\circ}$
Square - like shape	4	4	$90^{\circ}$
Irregular shape	0	1	$360^{\circ}$
Regular Pentagon	5	5	$72^{\circ}$
Curved - shape	1	1	$360^{\circ}$
Arrow - like shape	1	1	$360^{\circ}$
Ellipse	2	2	$180^{\circ}$
Star - like shape	4	4	$90^{\circ}$
Regular Hexagon	6	6	$60^{\circ}$
5 - pointed star	5	5	$72^{\circ}$