for questions 19-22, use the figure below. 19. what is the name of the shape on the left? 20. how many lines of symmetry are there on the shape to the left? 21. list all of the degrees of rotational symmetry for the shape to the left. 22. how many diagonals does the regular polygon have? for questions 23-26 draw the following 23. draw all lines of symmetry on the square. 24. draw all the diagonals on the square. 25. draw all lines of symmetry on the parallelogram. 26. draw all diagonals on the parallelogram.

Question

Accepted Answer

### Question 19:
# Explanation:
## Step1: Identify the shape
The figure is a regular octagon, which has 8 equal sides and 8 equal angles.
# Answer:
Regular Octagon

### Question 20:
# Explanation:
## Step1: Recall line symmetry in regular octagon
A regular $ n $-sided polygon has $ n $ lines of symmetry. For an octagon, $ n = 8 $. So it has 8 lines of symmetry (4 through opposite vertices, 4 through mid - points of opposite sides).
# Answer:
8

### Question 21:
# Explanation:
## Step1: Recall rotational symmetry formula
The formula for the angle of rotational symmetry of a regular $ n $-sided polygon is $ \theta=\frac{360^{\circ}}{n} $. For a regular octagon, $ n = 8 $, so $ \theta=\frac{360^{\circ}}{8} = 45^{\circ} $.
## Step2: List all rotational symmetries
The rotational symmetries are the multiples of $ 45^{\circ} $ that are less than $ 360^{\circ} $. So the angles are $ 45^{\circ},90^{\circ},135^{\circ},180^{\circ},225^{\circ},270^{\circ},315^{\circ} $.
# Answer:
$ 45^{\circ},90^{\circ},135^{\circ},180^{\circ},225^{\circ},270^{\circ},315^{\circ} $

### Question 22:
# Explanation:
## Step1: Recall diagonal formula for polygon
The formula for the number of diagonals $ d $ of a polygon with $ n $ sides is $ d=\frac{n(n - 3)}{2} $. For a regular octagon, $ n = 8 $.
## Step2: Substitute $ n = 8 $ into the formula
$ d=\frac{8\times(8 - 3)}{2}=\frac{8\times5}{2}=20 $
# Answer:
20

### Question 23:
# Explanation:
## Step1: Recall lines of symmetry in square
A square has 4 lines of symmetry: 2 diagonals and 2 lines through the mid - points of opposite sides.
## Step2: Draw the lines
- Draw a vertical line through the mid - points of $ AB $ and $ CD $.
- Draw a horizontal line through the mid - points of $ AD $ and $ BC $.
- Draw the two diagonals $ AC $ and $ BD $.
# Answer:
The square has 4 lines of symmetry: 2 through mid - points of opposite sides and 2 diagonals (visualized by drawing these lines on the square).

### Question 24:
# Explanation:
## Step1: Recall diagonals in square
A square has 2 diagonals, which are the line segments connecting opposite vertices.
## Step2: Draw the diagonals
Draw the line segments $ AC $ and $ BD $ (connecting vertex $ A $ to $ C $ and vertex $ B $ to $ D $).
# Answer:
The square has 2 diagonals (drawn as $ AC $ and $ BD $).

### Question 25:
# Explanation:
## Step1: Recall lines of symmetry in parallelogram
A non - special parallelogram (not a rhombus, rectangle, or square) has 0 lines of symmetry. If it is a rhombus (a type of parallelogram with all sides equal), it has 2 lines of symmetry (the diagonals). If it is a rectangle (a type of parallelogram with all angles $ 90^{\circ} $), it has 2 lines of symmetry (through mid - points of opposite sides). Assuming a general parallelogram (not rhombus or rectangle), the number of lines of symmetry is 0.
## Step2: Draw (or state) the lines
Since there are no lines of symmetry (for a general parallelogram), we note that. If it is a rhombus, draw the two diagonals; if it is a rectangle, draw the two lines through mid - points of opposite sides.
# Answer:
A general parallelogram has 0 lines of symmetry. (If it is a rhombus: 2 lines of symmetry (diagonals); if it is a rectangle: 2 lines of symmetry (through mid - points of opposite sides))

### Question 26:
# Explanation:
## Step1: Recall diagonals in parallelogram
A parallelogram has 2 diagonals, which are the line segments connecting opposite vertices.
## Step2: Draw the diagonals
Draw the line segments connecting the opposite vertices (e.g., if the parallelogram has vertices $ W,X,Y,Z $ in order, draw $ WY $ and $ XZ $).
# Answer:
The parallelogram has 2 diagonals (drawn by connecting opposite vertices).

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QUESTION IMAGE

Question

Explanation:

Question 19:

Step1: Identify the shape

Step1: Recall line symmetry in regular octagon

Step1: Recall rotational symmetry formula

Step2: List all rotational symmetries

Answer:

Question 20: