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9-12 Geometry Unit 1 Lesson 22

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

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

Unit

•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

Lesson

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

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

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

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Unit 1, Lesson 22

Now What Can You Build? (Optional)

Geometry

Practice

Problem 1
Student Task Statement
This design began from the construction of a regular hexagon. Name 2 pairs of congruent figures.

Hexagon A B C D E F. Vertical line segments B D and A E are drawn. Diagonal line segment C G is drawn, with G on line B D, creating triangles B C G and C D G . Diagonal line segment F H is drawn, with H on line A E, creating triangles E F H and A F H.

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Problem 2

Student Task Statement

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

Student Task Statement

Noah starts with triangle and makes 2 new triangles by translating to and by translating to . Noah thinks that triangle is congruent to triangle . 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

Student Task Statement

In the image, triangle is congruent to triangle and triangle . What are the measures of the 3 angles in triangle ? 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

Student Task Statement

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 and 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

Student Task Statement

In this diagram, point is the midpoint of segment , and is the image of by a rotation of around .

Explain why rotating using center takes to .
Explain why angles and 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

Student Task Statement

Lines and are perpendicular. The dashed rays bisect angles and .

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 is congruent to angle .

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Problem 8

ForLesson 19: Evidence, Angles, and Proof

Student Task Statement

Lines and meet at point .

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

Student Task Statement

Draw the image of triangle after this sequence of rigid transformations.

Reflect across line segment .
Translate by directed line segment , which starts at .

<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

Student Task Statement

Draw the image of figure after a clockwise rotation around point using angle and then a translation by directed line segment .
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

Angle is obtuse.

Angle is congruent to angle .

Angle is congruent to angle .

Angle is 45 degrees.