Lesson 17

Working with Rigid Transformations

Problem 1

Quadrilateral $$ABCD$$ is congruent to quadrilateral $$A’B’C’D’$$. Describe a sequence of rigid motions that takes $$A$$ to $$A’$$, $$B$$ to $$B’$$, $$C$$ to $$C’$$, and $$D$$ to $$D’$$.

Solution

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Problem 2

Select all transformations that must take any point $$A$$ to any point $$B$$.

A:

Rotation of $$180^\circ$$around $$A$$

B:

Rotation of $$180^\circ$$around $$B$$

C:

Rotation of $$180^\circ$$around the midpoint of segment $$AB$$

D:

Reflection across the line $$AB$$

E:

Reflection across the perependicular bisector of segment $$AB$$

F:

Translation by the directed line segment $$AB$$

G:

Translation by the directed line segment $$BA$$

Solution

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Problem 3

Triangle $$ABC$$ is congruent to triangle $$A’B’C’$$. Describe a sequence of rigid motions that takes $$A$$ to $$A’$$, $$B$$ to $$B’$$, and $$C$$ to $$C’$$.

Solution

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Problem 4

A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this.

A:

All sides of the triangle have the same length.

B:

All angles of the triangle have the same measure.

C:

All rotations take one half of the triangle to the other half of the triangle.

D:

It is a right triangle.

E:

None of the sides of the triangle have the same length.

F:

None of the angles of the triangle have the same measure.

Solution

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(From Unit 1, Lesson 16.)

Problem 5

Select all the angles of rotation that produce symmetry for this flower.

A:

30

B:

45

C:

60

D:

90

E:

120

F:

135

G:

180

Solution

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(From Unit 1, Lesson 16.)

Problem 6

A right triangle has a line of symmetry. Select all conclusions that must be true.

A:

All sides of the triangle have the same length.

B:

All angles of the triangle have the same measure.

C:

Two sides of the triangle have the same length.

D:

Two angles of the triangle have the same measure.

E:

No sides of the triangle have the same length.

F:

No angles of the triangle have the same measure.

Solution

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(From Unit 1, Lesson 15.)

Problem 7

In quadrilateral $$BADC$$, $$AB=AD$$ and $$BC=DC$$. The line $$AC$$ is a line of symmetry for this quadrilateral. Based on the line of symmetry, explain why angles $$ACB$$ and $$ACD$$ have the same measure.

Solution

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(From Unit 1, Lesson 15.)

Problem 8

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

A:

Construct the midpoint of segment $$AB$$.

B:

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

C:

Construct a line tangent to circle $$A$$ with radius $$AB$$.

D:

Construct a vertical line passing through point $$A$$ and a horizontal line passing through point $$B$$.

Solution

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(From Unit 1, Lesson 11.)

Problem 9

Here is triangle $$POG$$. Match the description of the rotation with the image of $$POG$$ under that rotation.

Solution

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(From Unit 1, Lesson 13.)