Question

1. match each description to its correct image.

no lines of symmetry
one line of symmetry
two lines of symmetry
three lines of symmetry

1. how many lines of symmetry does this figure have?

(figure of an octagon)
options: 1, 2, 4, 8

1. letters examine each capital letter in the alphabet. determine which letters have 180° rotational symmetry about a point in the center of the letter.

options: h, i, n, o, s, x, z; g, j, m, o, p, r, z; b, e, h, j, f, y, z; a, c, i, o, u, v, y

1. triangle def has coordinates d(4, −1), e(5, 2), and f(1, 2). determine the coordinates of the vertices of the image after a reflection in the y - axis.

options: d(4, 1), e(5, −2), and f(1, −2); d(5, −1), e(6, 2), and f(2, 2); d(−4, −1), e(−5, 2), and f(−1, 2); d(1, 0), e(2, 3), and f(−2, 3)

Explanation:

Question 5

• No lines of symmetry: The parallelogram (the last figure) has no lines of symmetry as it can't be folded to match halves.
• One line of symmetry: The trapezoid (second figure) has one line of symmetry (if it's isosceles trapezoid, which this looks like).
• Two lines of symmetry: The rectangle (first figure) has two lines of symmetry (vertical and horizontal).
• Three lines of symmetry: The equilateral triangle (third figure) has three lines of symmetry (each from a vertex to midpoint of opposite side).

Step1: Identify the figure

The figure is a regular octagon. A regular polygon with \( n \) sides has \( n \) lines of symmetry.

Step2: Calculate lines of symmetry

For a regular octagon, \( n = 8 \), so it has 8 lines of symmetry.

A letter has \( 180^\circ \) rotational symmetry if rotating it \( 180^\circ \) gives the same letter.

• H: Rotates to H.
• I: Rotates to I.
• N: Rotates to N.
• O: Rotates to O.
• S: Rotates to S.
• X: Rotates to X.
• Z: Rotates to Z.

Other options have letters that don't have \( 180^\circ \) symmetry (e.g., G, J, M, P, R in second option; B, E, F, Y in third; A, C, U, V, Y in fourth).

Answer:

• No lines of symmetry: The parallelogram (bottom figure)
• One line of symmetry: The trapezoid (second figure)
• Two lines of symmetry: The rectangle (top figure)
• Three lines of symmetry: The equilateral triangle (third figure)

Question 6