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9-12 Geometry Unit 1 Lesson 22

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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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 Lesson 20 Lesson 21 •Lesson 22

K-5
6-8
9-12

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Geometry
Algebra 2
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Integrated Math 1
Integrated Math 2
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Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
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Lesson 16
Lesson 17
Lesson 18
Lesson 19
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Lesson 21
Lesson 22

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Unit 1, Lesson 22

Now What Can You Build? (Optional)

Geometry

Practice

Problem 1

This design began from the construction of a regular hexagon. Name 2 pairs of congruent figures.

<p>Hexagon with line segments.</p>

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Problem 2

This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure to itself.

<p>Regular hexagon with center I and vertices A B C D E F. Segment F C contains points H I G. Segment A E passes through H. Segment B D passes through G. Segment B E passes through I. Triangles I H E and I G B are highlighted.</p>

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Problem 3

ForLesson 21: One Hundred Eighty

Noah starts with triangle \(ABC\) and makes 2 new triangles by translating \(B\) to \(A\) and by translating \(B\) to \(C\). Noah thinks that triangle \(DCA\) is congruent to triangle \(BAC\). Do you agree with Noah? Explain your reasoning.

<p>Large triangle BFE has small triangle ADC at its midpoints.</p>

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Problem 4

ForLesson 21: One Hundred Eighty

In the image, triangle \(ABC\) is congruent to triangle \(BAD\) and triangle \(CEA\). What are the measures of the 3 angles in triangle \( CEA\)? Show or explain your reasoning.

<p>Trapezoid DECB base BC and point A midpoint of DE making triangle ABC. Angle D is 45 degrees and angle BAC is 75 degrees.</p>

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Problem 5

ForLesson 20: Transformations, Transversals, and Proof

In the figure shown, Angle 3 is congruent to Angle 6. Select all statements that must be true.

<p>Parallel lines f and g cut by a transversal, creating angles 1, 2, 3 and 4 at intersection of lines g and transversal, and creating angles 5, 6, 7 and 8 at intersection of lines f and transversal.</p>

Lines \(f\) and \(g\) are parallel.
Angle 2 is congruent to Angle 6.
Angle 2 and Angle 5 are supplementary.
Angle 1 is congruent to Angle 7.
Angle 4 is congruent to Angle 6.

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Problem 6

ForLesson 20: Transformations, Transversals, and Proof

In this diagram, point \(M\) is the midpoint of segment \(AC\), and \(B’\) is the image of \(B\) by a rotation of \(180^\circ\) around \(M\).

Explain why rotating \(180^\circ\) using center \(M\) takes \(A\) to \(C\).
Explain why angles \(BAC\) and \(B’CA\) have the same measure.

<p>Point M is the midpoint of segment AC and B Prime is the image of B by a rotation of 180 degrees around Point M.</p>

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Problem 7

ForLesson 19: Evidence, Angles, and Proof

Lines \(AB\) and \(BC\) are perpendicular. The dashed rays bisect angles \(ABD\) and \(CBD\).

Select all statements that must be true:

<p>Lines AB and BC are perpendicular and meet at point B. Dashed rays BF and BE bisect angles ABD and CBD.</p>

Angle \(CBF\) is congruent to angle \(DBF\).
Angle \(CBE\) is obtuse.
Angle \(ABC\) is congruent to angle \(EBF\).
Angle \(DBC\) is congruent to angle \(EBF\).
Angle \(EBF\) is 45 degrees.

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Problem 8

ForLesson 19: Evidence, Angles, and Proof

Lines \(AD\) and \(EC\) meet at point \(B\).

Give an example of a rotation using an angle greater than 0 degrees and less than 360 degrees that takes both lines to themselves. Explain why your rotation works.

<p>Lines AD and EC intersect at point B.</p>

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Problem 9

ForLesson 18: Practicing Point-by-Point Transformations

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 \(B\).

<p>Triangle ABC with directed line segment <em>u</em> formed by ray BA.</p>

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Problem 10

ForLesson 18: Practicing Point-by-Point Transformations

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

<p>A figure CAST as a rectangle with missing side CT on the bottom.</p>

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Lesson 22 Resources

Student Materials