Curriculum / Math / 10th Grade / Unit 1: Constructions, Proof, and Rigid Motion / Lesson 9
Math
Unit 1
10th Grade
Lesson 9 of 19
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Describe rigid motions. Use algebraic rules to translate points and line segments and describe translations on the coordinate plane.
The core standards covered in this lesson
G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.B.6 — Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
The foundational standards covered in this lesson
8.G.A.1 — Verify experimentally the properties of rotations, reflections, and translations:
8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Below are points $$A$$ and $$B$$. Translate each of these points two units right and three units down.
The notation $${(x,y) \rightarrow (x+2,y-3)}$$ is used to describe the translation you have just performed. Explain this notation.
Line segment $${\overline{CD}}$$ has endpoints of $${C (-1,-3)}$$ and $${D (-1,2)}$$.
Translate this segment according to the rule $${(x,y) \rightarrow (x-2, y-3)}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Translate the line segment formed by the endpoints $${E(0, 2)}$$ $${F (1,-4)}$$ according to the rule $${(x,y) \rightarrow (x+5, y+4)}$$.
Lesson 8
Lesson 10
Topic A: Constructions of Basic Geometric Figures
Describe the precise definition and notation for foundational geometric figures.
G.CO.A.1
Construct an equilateral triangle with only a straight-edge and a compass. Copy a line segment.
G.CO.A.1 G.CO.D.12 G.CO.D.13
Construct, bisect, and copy an angle.
G.CO.A.1 G.CO.D.12
Construct a perpendicular bisector.
Construct the altitudes and perpendicular bisectors of sides of triangles.
G.CO.C.10 G.CO.D.12
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Topic B: Justification and Proof of Angle Measure
Use principles of proof to justify each step in solving an equation.
A.REI.A.1
Use angle relationships around a point to find missing measures. Prove angle relationships around a point using geometric statements and reasons.
G.CO.C.9
Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships
Describe and identify rigid motions.
G.CO.A.1 G.CO.A.2 G.CO.B.6
G.CO.A.2 G.CO.B.6
Translate points and line segments not on the coordinate plane using constructions. Describe properties of translations with respect to line segments and angles.
G.CO.A.2 G.CO.A.4 G.CO.A.5
Construct parallel lines. Prove the relationship between corresponding angles. Use this relationship to find missing measures directly and algebraically.
G.CO.A.1 G.CO.A.4 G.CO.C.9 G.CO.D.12
Prove angle relationships in parallel line diagrams.
G.CO.A.1 G.CO.C.9
Construct auxiliary parallel lines and use these in the development of proofs and identification of missing measures.
G.CO.C.9 G.CO.D.12
Topic D: Reflections and Rotations of Points, Line Segments, and Angles
Perform reflections on a coordinate plane across axes and other defined lines. Identify characteristics and an algebraic rule for the reflection.
G.CO.A.2 G.CO.A.4 G.CO.A.5 G.CO.B.6
Use construction and patty paper to reflect a figure not on the coordinate plane. Describe the properties of a reflection.
Perform rotations on a coordinate plane. Identify characteristics and algebraic rules for the rotation.
Use construction and patty paper to rotate a figure not on the coordinate plane. Describe the properties of a rotation.
G.CO.A.2 G.CO.A.5 G.CO.B.6
Describe a sequence of rigid motions that will map a point, line segment, or angle onto another figure.
G.CO.A.5 G.CO.B.6
Describe rigid motions, or sequences of rigid motions that have the same effect on a figure.
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