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9-12 Integrated Math 1 Unit 1 Lesson 18

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K-5 Math 6-8 Math •9-12 Math

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 •Lesson 18 Lesson 19

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Unit 1, Lesson 18

Practicing Point-by-Point Transformations (Optional)

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Integrated Math 1

Practice

Problem 1

The figures are congruent. Select all the sequences of transformations that would take Figure 1 to Figure 2.

<p>Two figures on a grid.</p>

Translate by directed line segment \(AD\).
Rotate 180 degrees around point \(E\).
Translate by directed line segment \(AE\), and reflect across \(AC\).
Translate by directed line segment \(CE\), and rotate 90 degrees counterclockwise around point \(E\).
Rotate 180 degrees around point \(C\), translate by directed line segment \(CE\), then reflect across segment \(EF\).
Reflect across segment \(AB\), rotate clockwise by angle \(BFE\) using center \(F\), then reflect across segment \(EF\).

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Problem 2

Draw the image of figure \(ACTS\) after a clockwise rotation around point \(T\) by angle \(CTS\) and then a translation by directed line segment \(CT\).
Describe another sequence of transformations that will result in the same image.

<p>A figure formed by 3 line segments, looks like the letter U. 4 points on the endpoints of the segments. Starting at the top left, A. Moving downard, C. Moving to the right, T. Moving upward, S.</p>

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Problem 3

Draw the image of triangle \(ABC\) after this sequence of rigid transformations.

Reflect across line segment \(AB\).
Translate by directed line segment \(u\), which starts at \(A\).

<p>Triangle A B C.</p>

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Problem 4

ForLesson 17: Working with Rigid Transformations

Describe a transformation that takes any point \(A\) to any point \(B\).

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Problem 5

ForLesson 17: Working with Rigid Transformations

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 \(C’\).

<p>Congruent triangles A B C and A prime B prime C prime.</p>

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Problem 6

ForLesson 16: More Symmetry

A quadrilateral 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.

All sides of the quadrilateral have the same length.
All angles of the quadrilateral have the same measure.
All rotations take one half of the quadrilateral to the other half of the quadrilateral.

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Problem 7

ForLesson 15: Symmetry

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

All sides of the quadrilateral have the same length.
All angles of the quadrilateral have the same measure.
Two sides of the quadrilateral have the same length.
Two angles of the quadrilateral have the same measure.
No sides of the quadrilateral have the same length.
No angles of the quadrilateral have the same measure.

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Problem 8

ForLesson 14: Defining Rotations

Which segment is the image of \(FG\) when rotated \(90^\circ\) clockwise around point \(P\)?

<p>Segments on a grid.</p>

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Problem 9

ForLesson 12: Defining Translations

Which statement is true about a translation?

A translation rotates a line.
A translation takes a line to a parallel line or itself.
A translation takes a line to a perpendicular line.
A translation dilates a line.

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Lesson 18 Resources

Student Materials Student Materials in Spanish