Download M1 Lesson 21 - Spokane Public Schools

Lesson 21
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Example
തതതത is one diagonal of the square. ᇞ ‫ ܥܤܣ‬is a reflection of ᇞ ‫ ܥܦܣ‬across segment ‫ܥܣ‬. Complete
‫ ܦܥܤܣ‬is a square, and ‫ܥܣ‬
the table below, identifying the missing corresponding angles and sides.
Corresponding Angles
‫ ܥܣܤס‬՜
‫ ܥܤܣס‬՜
‫ ܣܥܤס‬՜
a.
Corresponding Sides
തതതത
‫ ܤܣ‬՜
തതതത
‫ ܥܤ‬՜
തതതത ՜
‫ܥܣ‬
Are the corresponding sides and angles congruent? Justify your response.
b. Is ᇞ ‫ ܥܤܣ‬؆ᇞ ‫ ?ܥܦܣ‬Justify your response.
Lesson 21:
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Correspondence and Transformations
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Lesson 21
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Exercises
Each exercise below shows a sequence of rigid motions that map a pre-image onto a final image. Identify each rigid
motion in the sequence, writing the composition using function notation. Trace the congruence of each set of
corresponding sides and angles through all steps in the sequence, proving that the pre-image is congruent to the final
image by showing that every side and every angle in the pre-image maps onto its corresponding side and angle in the
image. Finally, make a statement about the congruence of the pre-image and final image.
1.
Sequence of Rigid
Motions (2)
Composition in
Function Notation
Sequence of
Corresponding Sides
Sequence of
Corresponding Angles
Triangle Congruence
Statement
2.
Sequence of Rigid
Motions (2)
Composition in
Function Notation
Sequence of
Corresponding Sides
Sequence of
Corresponding Angles
Triangle Congruence
Statement
Lesson 21:
© 2015 Great Minds.. eureka-math.org
GEO-M1-SE-1.3.0-06.2015
Correspondence and Transformations
S.117
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 21
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
3.
Sequence of Rigid
Motions (2)
Composition in
Function Notation
Sequence of
Corresponding Sides
Sequence of
Corresponding Angles
Triangle Congruence
Statement
Lesson 21:
© 2015 Great Minds.. eureka-math.org
GEO-M1-SE-1.3.0-06.2015
Correspondence and Transformations
S.118
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 21
M1
GEOMETRY
Problem Set
1. Exercise 3 mapped ᇞ ‫ ܥܤܣ‬onto ᇞ ܻܼܺ in three steps. Construct a fourth step that would map ᇞ ܻܼܺ back onto ᇞ
‫ܥܤܣ‬.
2. Explain triangle congruence in terms of rigid motions. Use the terms corresponding sides and corresponding angles
in your explanation.
Lesson 21:
© 2015 Great Minds.. eureka-math.org
GEO-M1-SE-1.3.0-06.2015
Correspondence and Transformations
S.119
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.