The regular octagon at the right is divided into eight congruent
triangles. Find the image of the given point or segment for the given
rotation or reflection.
1. point A; a 90 rotation about the center G
2. point H; a 180 rotation about the center D
3. 𝑨𝑩; a reflection in 𝑨𝑬
𝑨𝑯
4. 𝑮𝑯; a reflection in 𝑨𝑬
𝑪𝑩
Lesson Objective: Identify the type of symmetry in a figure.
VOCABULARY
A figure has symmetry if there is an isometry that maps the figure
onto itself.
If the isometry is the reflection of a plane figure, the figure has
reflectional symmetry or line symmetry .
symmetry
reflectional
line
5/19/2015 12:38:13 PM
GEOMETRY/C.Bautista
Lesson Objective: Identify the type of symmetry in a figure.
Draw all lines of symmetry for the isosceles trapezoid.
Draw any lines that divide the isosceles trapezoid
so that half of the figure is a mirror image of the
other half.
There is one line of symmetry.
Draw a rectangle and all of its lines of symmetry.
Lesson Objective: Identify the type of symmetry in a figure.
A figure that has rotational symmetry is its own image for some
rotation of 180° or less.
A figure that has point symmetry has 180 rotational symmetry.
The figure is its own image after one halfturn, so it has rotational symmetry with
a 180 angle of rotation.
The figure also has point symmetry.
Lesson Objective: Identify the type of symmetry in a figure.
Judging from appearance, do the letters V and H have rotational
symmetry? If so, give an angle of rotation.
V
The letter V does not have rotational symmetry because
it must be rotated 360° before it is its own image.
The letter H is its own image after one half-turn, so it has
rotational symmetry with a 180° angle of rotation.
a. Judging from appearance, tell whether the figure at
the left has rotational symmetry. If so, give the angle of
rotation. yes; 180
b. Does the figure have point symmetry?
yes
H
Lesson Objective: Identify the type of symmetry in a figure.
A nut holds a bolt in place. Some nuts have square
faces, like the top view shown below. Tell whether the nut has
rotational symmetry and/or reflectional symmetry. Draw all lines of
symmetry.
The nut has a square outline with a circular
opening. The square and circle are concentric.
The nut is its own image after one quarter-turn,
so it has 90° rotational symmetry.
The nut has 4 lines of symmetry.
Lesson Objective: Identify the type of symmetry in a figure.
Tell whether the umbrella has rotational
symmetry about a line and/or reflectional
symmetry.
rotational and reflectional symmetry
Tell whether each three-dimensional object has rotational symmetry
about a line and/or reflectional symmetry in a plane.
reflectional symmetry
both reflectional &
rotational symmetry
Draw all lines of symmetry for each figure.
no line of symmetry
Judging from appearance, tell what type(s) of symmetry each figure
has. If it has line symmetry, sketch the figure and the line(s) of
symmetry. If it has rotational symmetry, state the angle of rotation.
line symmetry
line symmetry
72° rotational symmetry
line symmetry
90° rotational symmetry
Judging from appearance, tell what type(s) of symmetry each figure
has. If it has line symmetry, sketch the figure and the line(s) of
symmetry. If it has rotational symmetry, state the angle of rotation.
line symmetry
180° rotational symmetry
line symmetry
45° rotational symmetry
Judging from appearance, tell what type(s) of symmetry each figure
has. If it has line symmetry, sketch the figure and the line(s) of
symmetry. If it has rotational symmetry, state the angle of rotation.
Each diagram shows a figure folded along a line of symmetry. Sketch
the unfolded figure.