QUESTION IMAGE
Question
a. is the line drawn a symmetry line for the figure? a. b. c. d. e. f. yes or no yes or no yes or no yes or no yes or no yes or no b. fill in the table below giving all the information about reflection and rotational symmetry. draw dotted lines to indicate lines of symmetry. if the figure has line symmetry, draw them line symmetry? yes no yes no yes no yes no yes no yes no # of lines of reflection rotational symmetry? yes no yes no yes no yes no yes no yes no order of rotation angle of rotation figure line symmetry? yes no yes no yes no yes no yes no yes no # of lines of reflection rotational symmetry? yes no yes no yes no yes no yes no yes no order of rotation angle of rotation
Step1: Recall line - symmetry definition
A line of symmetry divides a figure into two congruent parts such that one part is the mirror - image of the other.
Step2: Analyze part A figures
a.
The figure has a line that divides it into two mirror - image parts, so the answer is Yes.
b.
The diagonal line does not divide the square into two mirror - image parts (because of the different orientations of the square's sides relative to the diagonal), so the answer is No.
c.
The vertical line divides the rectangle into two mirror - image parts, so the answer is Yes.
d.
The vertical line divides the heart into two mirror - image parts, so the answer is Yes.
e.
The diagonal line does not divide the triangle into two mirror - image parts (assuming it's a non - isosceles right triangle as drawn), so the answer is No.
f.
The vertical line divides the isosceles triangle into two mirror - image parts, so the answer is Yes.
Step3: Analyze part B figures for line symmetry
'M'
It has 1 line of symmetry (a vertical line through the middle).
Star
It has 5 lines of symmetry.
Spiral
It has no line of symmetry.
Heart
It has 1 line of symmetry (a vertical line through the middle).
Circular figure with arrows
It has no line of symmetry.
Christmas tree
It has 1 line of symmetry (a vertical line through the middle).
Hexagon
It has 6 lines of symmetry.
'Y' figure
It has 3 lines of symmetry.
10 of spades
It has 1 line of symmetry (a vertical line through the middle).
Oval
It has 2 lines of symmetry (a vertical and a horizontal line).
Parallelogram
It has no line of symmetry.
Trapezoid
It has 0 or 1 line of symmetry (if isosceles, 1; if not, 0). Assuming non - isosceles here, so 0.
Octagon
It has 8 lines of symmetry.
'S'
It has no line of symmetry.
Step4: Analyze part B figures for rotational symmetry
'M'
No rotational symmetry (order 1, but we usually don't consider order 1 as rotational symmetry in a non - trivial sense).
Star
Order of rotation is 5, angle of rotation is $\frac{360^{\circ}}{5}=72^{\circ}$.
Spiral
Has rotational symmetry of infinite order (because it can be rotated by any angle and still look the same in a sense, but if we consider non - continuous rotation, order is 1 non - trivially). Let's assume non - trivial case, order 1.
Heart
No rotational symmetry (order 1).
Circular figure with arrows
No rotational symmetry (order 1).
Christmas tree
No rotational symmetry (order 1).
Hexagon
Order of rotation is 6, angle of rotation is $\frac{360^{\circ}}{6}=60^{\circ}$.
'Y' figure
Order of rotation is 3, angle of rotation is $\frac{360^{\circ}}{3}=120^{\circ}$.
10 of spades
No rotational symmetry (order 1).
Oval
Order of rotation is 2, angle of rotation is $\frac{360^{\circ}}{2}=180^{\circ}$.
Parallelogram
Order of rotation is 2, angle of rotation is $\frac{360^{\circ}}{2}=180^{\circ}$.
Trapezoid
No rotational symmetry (order 1).
Octagon
Order of rotation is 8, angle of rotation is $\frac{360^{\circ}}{8}=45^{\circ}$.
'S'
Order of rotation is 2, angle of rotation is $\frac{360^{\circ}}{2}=180^{\circ}$.
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Part A
a. Yes
b. No
c. Yes
d. Yes
e. No
f. Yes
Part B
| Figure | Line Symmetry? | # of Lines of Reflection | Rotational Symmetry? | Order of Rotation | Angle of Rotation |
|---|---|---|---|---|---|
| Star | Yes | 5 | Yes | 5 | $72^{\circ}$ |
| Spiral | No | 0 | No | 1 | N/A |
| Heart | Yes | 1 | No | 1 | N/A |
| Circular figure with arrows | No | 0 | No | 1 | N/A |
| Christmas tree | Yes | 1 | No | 1 | N/A |
| Hexagon | Yes | 6 | Yes | 6 | $60^{\circ}$ |
| 'Y' figure | Yes | 3 | Yes | 3 | $120^{\circ}$ |
| 10 of spades | Yes | 1 | No | 1 | N/A |
| Oval | Yes | 2 | Yes | 2 | $180^{\circ}$ |
| Parallelogram | No | 0 | Yes | 2 | $180^{\circ}$ |
| Trapezoid | No | 0 | No | 1 | N/A |
| Octagon | Yes | 8 | Yes | 8 | $45^{\circ}$ |
| 'S' | No | 0 | Yes | 2 | $180^{\circ}$ |