Geometry: An Interactive Journey to Mastery

Summary
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Example 1
Explain why a translation is an isometry.
Solution
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distance d in parallel directions, takes points A and
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Quadrilateral AABBcc has one pair of sides that are both congruent and parallel. By Problem 2 of Lesson 14, the
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that AB A Bcc. Thus, the translation has preserved the distance between points.
Example 2
Identify all the symmetries of a regular pentagon. How many line symmetries does it have? How many
rotational symmetries does it have?
Solution
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symmetries, rotations of 72°, 144°, 216°, and 288°
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rotational symmetries if they choose to include the
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Example 3
Prove that a dilation maps three collinear points to three collinear positions.

d

A d

Aƍ

Bƍ

B

Figure 30.1

72°

Figure 30.2