SYMMETRY Section 12 5 Geometry Pre AP Revised

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SYMMETRY Section 12– 5 Geometry Pre. AP, Revised © 2013 viet. dang@humble. k 12.

SYMMETRY Section 12– 5 Geometry Pre. AP, Revised © 2013 viet. dang@humble. k 12. tx. us 9/18/2021 1: 01 AM 12– 5: Symmetry 1

SYMMETRY A. Symmetry is a transformation of the figure where the image coincides with

SYMMETRY A. Symmetry is a transformation of the figure where the image coincides with the pre -image. 1. Line of Symmetry is a line that divides the figure into two congruent halves 2. Rotational Symmetry can be rotated around a point by a certain number of degrees so that the image ends up to be exactly the same as the pre-image. 3. Plane Symmetry is a three-dimensional figure has if a plane can divide the figure into two congruent reflected halves. 9/18/2021 1: 01 AM 12– 5: Symmetry 2

LINE SYMMETRY 9/18/2021 1: 01 AM 12– 5: Symmetry 3

LINE SYMMETRY 9/18/2021 1: 01 AM 12– 5: Symmetry 3

EXAMPLE 1 For each figure find (one of) the line(s) of symmetry. Write the

EXAMPLE 1 For each figure find (one of) the line(s) of symmetry. Write the equation of the line of symmetry. 9/18/2021 1: 01 AM 12– 5: Symmetry 4

EXAMPLE 2 For each figure find (one of) the line(s) of symmetry. Identify the

EXAMPLE 2 For each figure find (one of) the line(s) of symmetry. Identify the amount of lines of symmetry. 9/18/2021 1: 01 AM 12– 5: Symmetry 5

EXAMPLE 3 For each figure find (one of) the line(s) of symmetry. Write the

EXAMPLE 3 For each figure find (one of) the line(s) of symmetry. Write the equation of the line of symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 6

YOUR TURN For each figure find (one of) the line(s) of symmetry. Write the

YOUR TURN For each figure find (one of) the line(s) of symmetry. Write the equation of the line of symmetry and the amount of lines of symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 7

ROTATIONAL SYMMETRY It is the smallest angle through which a figure can be rotated

ROTATIONAL SYMMETRY It is the smallest angle through which a figure can be rotated to coincide with itself. The number of times the figure coincides with itself as it rotates through 360° is called the order of the rotational symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 8

EXAMPLE 4 Tell whether each figure has rotational symmetry. If so, give the angle

EXAMPLE 4 Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 9

EXAMPLE 4 Tell whether each figure has rotational symmetry. If so, give the angle

EXAMPLE 4 Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 10

EXAMPLE 5 Tell whether each figure has rotational symmetry. If so, give the angle

EXAMPLE 5 Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 11

YOUR TURN Tell whether each figure has rotational symmetry. If so, give the angle

YOUR TURN Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. 9/18/2021 1: 02 AM 12– 5: Symmetry 12

PLANE VS. AXIS SYMMETRY A. Plane symmetry is a plane can divide a figure

PLANE VS. AXIS SYMMETRY A. Plane symmetry is a plane can divide a figure into two congruent halves. B. Symmetry About an Axis is where there is a line about which a figure can be rotated so that the image and preimage are identical. 9/18/2021 1: 02 AM 12– 5: Symmetry 13

PLANE SYMMETRY 9/18/2021 1: 02 AM 12– 5: Symmetry 14

PLANE SYMMETRY 9/18/2021 1: 02 AM 12– 5: Symmetry 14

AXIS SYMMETRY 9/18/2021 1: 02 AM 12– 5: Symmetry 15

AXIS SYMMETRY 9/18/2021 1: 02 AM 12– 5: Symmetry 15

EXAMPLE 6 Tell whether the figure has plane symmetry, symmetry about an axis, or

EXAMPLE 6 Tell whether the figure has plane symmetry, symmetry about an axis, or neither. 9/18/2021 1: 02 AM 12– 5: Symmetry 16

EXAMPLE 7 Tell whether the figure has plane symmetry, symmetry about an axis, or

EXAMPLE 7 Tell whether the figure has plane symmetry, symmetry about an axis, or neither. 9/18/2021 1: 02 AM 12– 5: Symmetry 17

YOUR TURN Tell whether the figure has plane symmetry, symmetry about an axis, or

YOUR TURN Tell whether the figure has plane symmetry, symmetry about an axis, or neither. Then, I want you to be prepared to defend your answer. 9/18/2021 1: 02 AM 12– 5: Symmetry 18

ASSIGNMENT Page 859 13 -18, 20 -25 all 9/18/2021 1: 02 AM 12– 5:

ASSIGNMENT Page 859 13 -18, 20 -25 all 9/18/2021 1: 02 AM 12– 5: Symmetry 19