8.9 Congruent Polygons

1
8.9 Congruent Polygons

• 6.4.9- I can identify congruent figures and use
  congruence to solve problems

2
You know that angles that have the same measure
are congruent. Congruent figures have the same
shape and same size. This means the corresponding
sides and corresponding angles are congruent.
3
Decide whether the figures in each pair are
congruent. If not, explain.
These figures do not have the same shape and they
are not the same size.
These figures are not congruent.
4
Decide whether the figures in each pair are
congruent. If not, explain.
These figures have the same shape and size.
These figures are congruent.
5
Check It Out Example 1A Decide whether the
figures in each pair are congruent. If not,
explain.
Each figure is a trapezoid. The corresponding
sides are 5.7 in., 7.5 in., 5 in., and 10 in.
These figures are congruent.
6
Jodi needs a sleeping pad that is congruent to
her sleeping bag. Which pad should she buy?
Both sleeping pads are trapezoids. Only sleeping
pad B is the same size as the sleeping bag.
Sleeping pad B is congruent to the sleeping bag.
7
8.10 Transformations

• 6.4.2 I can use translations, reflections, and
  rotations to transform geometric shapes

8
Vocabulary
transformation translation rotation reflection lin
e of reflection
9
A rigid transformation moves a figure without
changing its size or shape. So the original
figure and the transformed figure are always
congruent.
A translation is the movement of a figure along a
straight line.
A rotation is the movement of a figure around a
point. A point of rotation can be on or outside a
figure.
When a figure flips over a line, creating a
mirror image, it is called a reflection. The line
the figure is flipped over is called line of
reflection.
10
Tell whether each is a translation, rotation, or
reflection.
The figure is flipped over a line.
It is a reflection.
11
Tell whether each is a translation, rotation, or
reflection.
The figure moves around a point.
It is a rotation.
12
Tell whether each is a translation, rotation, or
reflection.
The figure is moved along a line.
It is a translation.
13
360
90
180
14
Additional Example 2A Drawing Transformations Dra
w each transformation. Draw a 180 rotation about
the point shown.
Trace the figure and the point of rotation. Place
your pencil on the point of rotation. Rotate the
figure 180. Trace the figure in its new location.
15
1. Tell whether the figure is translated,
rotated, or reflected. 2. Draw a vertical
reflection of the first figure in problem 1.
Lesson Quiz
rotated
16
Lesson Quiz for Student Response Systems
1. Identify the transformation of the figure.
A. translation B. reflection C. rotation
D. none
17
Lesson Quiz for Student Response Systems
2. Identify the horizontal reflection of the
figure. A. B. C. D.
18
8.11 Symmetry

• 6.4.2 I can identify symmetry

19
Vocabulary
line symmetry line of symmetry rotational
symmetry
20
A figure has line symmetry if it can be folded or
reflected so that the two parts of the figure
match, or are congruent. The line of reflection
is called the line of symmetry.
21
A figure has rotational symmetry if it can be
rotated about a point by an angle less than 360
so that it coincides with itself.
22
Determine whether each dashed line appears to be
a line of symmetry.
The two parts of the figure appear to match
exactly when folded or reflected across the line.
The line appears to be a line of symmetry.
23
Determine whether each dashed line appears to be
a line of symmetry.
The two parts of the figure do not appear
congruent.
The line does not appear to be a line of symmetry.
24
Find all of the lines of symmetry in the regular
polygon.
Count the lines of symmetry.
4 lines of symmetry
25
Tell whether each figure has rotational symmetry.
Each time the figure is rotated 90 about its
center, the image looks like the original figure.
The figure has rotational symmetry.
26
Tell whether each figure has rotational symmetry.
For any rotation less than 360, the image never
looks like the original figure.
The figure does not have rotational symmetry.