Lesson 11

Defining Reflections

Problem 1

Which of these constructions would construct a line of reflection that takes the point $$A$$ to point $$B$$?

A:

Construct the perpendicular bisector of segment $$AB$$.

B:

Construct a line through $$B$$ perpendicular to segment $$AB$$.

C:

Construct the line passing through $$A$$ and $$B$$.

D:

Construct a line parallel to line $$AB$$.

Solution

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Problem 2

A point $$P$$ stays in the same location when it is reflected over line $$\ell$$.

What can you conclude about $$P$$?

Solution

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Problem 3

Lines $$\ell$$ and $$m$$ are perpendicular with point of intersection $$P$$.

Noah says that a 180 degree rotation, with center $$P$$, has the same effect on points in the plane as reflecting over line $$m$$. Do you agree with Noah? Explain your reasoning.

Solution

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Problem 4

Here are 4 triangles that have each been transformed by a different transformation. Which transformation is not a rigid transformation?

Solution

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(From Unit 1, Lesson 10.)

Problem 5

There is a sequence of rigid transformations that takes $$A$$ to $$A’$$, $$B$$ to $$B’$$, and $$C$$ to $$C’$$. The same sequence takes $$D$$ to $$D’$$. Draw and label $$D’$$:

Solution

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(From Unit 1, Lesson 10.)

Problem 6

Here are 3 points in the plane. Explain how to determine whether point $$C$$ is closer to point $$A$$ or point $$B$$.

Solution

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(From Unit 1, Lesson 9.)

Problem 7

Diego says a quadrilateral with 4 congruent sides is always a regular polygon. Mai say it never is one. Do you agree with either of them?

Solution

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(From Unit 1, Lesson 7.)