Curriculum / Math / 10th Grade / Unit 1: Constructions, Proof, and Rigid Motion / Lesson 6

Constructions, Proof, and Rigid Motion

Lesson 6

Math

Unit 1

10th Grade

Lesson 6 of 19

Objective

Use principles of proof to justify each step in solving an equation.

Lesson Map

Topic A: Constructions of Basic Geometric Figures

Lesson

Describe the precise definition and notation for foundational geometric figures.

Standards

G.CO.A.1

Lesson

Construct an equilateral triangle with only a straight-edge and a compass. Copy a line segment.

Standards

G.CO.A.1G.CO.D.12G.CO.D.13

Lesson

Construct, bisect, and copy an angle.

Standards

G.CO.A.1G.CO.D.12

Lesson

Construct a perpendicular bisector.

Standards

G.CO.A.1G.CO.D.12

Lesson

Construct the altitudes and perpendicular bisectors of sides of triangles.

Standards

G.CO.C.10G.CO.D.12

Topic B: Justification and Proof of Angle Measure

Lesson

Use principles of proof to justify each step in solving an equation.

Standards

A.REI.A.1

Lesson

Use angle relationships around a point to find missing measures. Prove angle relationships around a point using geometric statements and reasons.

Standards

G.CO.C.9

Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships

Lesson

Describe and identify rigid motions.

Standards

G.CO.A.1G.CO.A.2G.CO.B.6

Lesson

Describe rigid motions. Use algebraic rules to translate points and line segments and describe translations on the coordinate plane.

Standards

G.CO.A.2G.CO.B.6

Lesson

Translate points and line segments not on the coordinate plane using constructions. Describe properties of translations with respect to line segments and angles.

Standards

G.CO.A.2G.CO.A.4G.CO.A.5

Lesson

Construct parallel lines. Prove the relationship between corresponding angles. Use this relationship to find missing measures directly and algebraically.

Standards

G.CO.A.1G.CO.A.4G.CO.C.9G.CO.D.12

Lesson

Prove angle relationships in parallel line diagrams.

Standards

G.CO.A.1G.CO.C.9

Lesson

Construct auxiliary parallel lines and use these in the development of proofs and identification of missing measures.

Standards

G.CO.C.9G.CO.D.12

Topic D: Reflections and Rotations of Points, Line Segments, and Angles

Lesson

Perform reflections on a coordinate plane across axes and other defined lines. Identify characteristics and an algebraic rule for the reflection.

Standards

G.CO.A.2G.CO.A.4G.CO.A.5G.CO.B.6

Lesson

Use construction and patty paper to reflect a figure not on the coordinate plane. Describe the properties of a reflection.

Standards

G.CO.A.2G.CO.A.4G.CO.A.5G.CO.B.6

Lesson

Perform rotations on a coordinate plane. Identify characteristics and algebraic rules for the rotation.

Standards

G.CO.A.2G.CO.A.4G.CO.A.5G.CO.B.6

Lesson

Use construction and patty paper to rotate a figure not on the coordinate plane. Describe the properties of a rotation.

Standards

G.CO.A.2G.CO.A.5G.CO.B.6

Lesson

Describe a sequence of rigid motions that will map a point, line segment, or angle onto another figure.

Standards

G.CO.A.5G.CO.B.6

Lesson

Describe rigid motions, or sequences of rigid motions that have the same effect on a figure.

Standards

G.CO.A.5G.CO.B.6

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