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8.9 Congruent Polygons
6.4.9- I can identify congruent figures and use congruence to
solve problems
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.
These figures do not have the same shape and they are not the same size.
These figures are not congruent.
Decide whether the figures in each pair are congruent. If not, explain.
Decide whether the figures in each pair are congruent. If not, explain.
These figures have the same shape and size.
These figures are congruent.
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.
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.
8.10 Transformations
6.4.2 – I can use translations, reflections, and rotations to
transform geometric shapes
Vocabulary
transformationtranslationrotationreflectionline of reflection
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.
Tell whether each is a translation, rotation, or reflection.
The figure is flipped over a line.
It is a reflection.
Tell whether each is a translation, rotation, or reflection.
The figure moves around a point.
It is a rotation.
Tell whether each is a translation, rotation, or reflection.
The figure is moved along a line.
It is a translation.
A full turn is a 360°
rotation. So a turn
is 90°, and a turn
is 180°.
12__
14__
90°
180°
360°
Additional Example 2A: Drawing Transformations
Draw 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.
Lesson Quiz
1. Tell whether the figure is translated, rotated, or
reflected.
2. Draw a vertical reflection of the first figure in
problem 1.
rotated
1. Identify the transformation of the figure.
A. translation B. reflection C. rotation D. none
Lesson Quiz for Student Response Systems
2. Identify the horizontal reflection of the figure.
A. B.
C. D.
Lesson Quiz for Student Response Systems
8.11 Symmetry
6.4.2 I can identify symmetry
Vocabulary
line symmetryline of symmetryrotational symmetry
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.
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.
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.
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.
Find all of the lines of symmetry in the regular polygon.
Count the lines of symmetry.
4 lines of symmetry
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.
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.
