Question

directions: for each design, determine if it has reflection symmetry. if it does, draw all of the lines of symmetry and write how many there are. 1. 2. 3. directions: determine if the figure has rotational symmetry. if it does, calculate and write all the degrees of rotation. 4. 5. 6. 7. 8. estimate the degree and direction of the rotation. 9. reflect the figure across the x - axis.

Explanation:

Step1: Analyze reflection symmetry of figure 1

The star - like figure has 4 lines of symmetry.

Step2: Analyze reflection symmetry of figure 2

The square - based figure has 4 lines of symmetry.

Step3: Analyze reflection symmetry of figure 3

The figure with heart - like shapes has 0 lines of symmetry.

Step4: Analyze rotational symmetry of figure 4 (pentagon)

The pentagon has rotational symmetry. The degrees of rotation are $72^{\circ},144^{\circ},216^{\circ},288^{\circ},360^{\circ}$ since $\frac{360^{\circ}}{5}=72^{\circ}$.

Step5: Analyze rotational symmetry of figure 5 (equilateral triangle)

The equilateral triangle has rotational symmetry. The degrees of rotation are $120^{\circ},240^{\circ},360^{\circ}$ since $\frac{360^{\circ}}{3}=120^{\circ}$.

Step6: Analyze rotational symmetry of figure 6 (circle)

The circle has infinite rotational symmetry. It can be rotated by any degree and still look the same.

Step7: Analyze rotational symmetry of figure 7 (diamond)

The diamond has rotational symmetry. The degrees of rotation are $180^{\circ},360^{\circ}$.

Step8: For figure 8, the estimate is correct

The apple is rotated $90^{\circ}$ clock - wise as indicated.

Step9: Reflect figure 9 across the x - axis

To reflect a point $(x,y)$ across the x - axis, the new point is $(x, - y)$. For triangle EFG, if $E(x_1,y_1)$, $F(x_2,y_2)$, $G(x_3,y_3)$, the reflected points are $E'(x_1,-y_1)$, $F'(x_2,-y_2)$, $G'(x_3,-y_3)$.

Answer:

1. 4 lines of symmetry
2. 4 lines of symmetry
3. 0 lines of symmetry
4. Rotational symmetry at $72^{\circ},144^{\circ},216^{\circ},288^{\circ},360^{\circ}$
5. Rotational symmetry at $120^{\circ},240^{\circ},360^{\circ}$
6. Infinite rotational symmetry
7. Rotational symmetry at $180^{\circ},360^{\circ}$
8. $90^{\circ}$ clock - wise rotation (as estimated)
9. Reflect points using $(x,y)\to(x, - y)$ to get new triangle.