Curriculum / Math / 10th Grade / Unit 1: Constructions, Proof, and Rigid Motion / Lesson 4
Math
Unit 1
10th Grade
Lesson 4 of 19
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Construct a perpendicular bisector.
The core standards covered in this lesson
G.CO.A.1 — Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.D.12 — Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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This lesson directly builds off the last lesson in the unit.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Bisect the following angle using constructions. Point $$A$$ should be considered the vertex of the angle.
$$\overline{CA}\cong \overline{AB}$$
Construct a perpendicular bisector for the following line segment. Write the steps of construction.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Geometry > Module 1 > Topic A > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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Construct the altitudes and perpendicular bisectors of sides of triangles.
Topic A: Constructions of Basic Geometric Figures
Describe the precise definition and notation for foundational geometric figures.
Standards
G.CO.A.1
Construct an equilateral triangle with only a straight-edge and a compass. Copy a line segment.
G.CO.A.1G.CO.D.12G.CO.D.13
Construct, bisect, and copy an angle.
G.CO.A.1G.CO.D.12
G.CO.C.10G.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.1G.CO.A.2G.CO.B.6
Describe rigid motions. Use algebraic rules to translate points and line segments and describe translations on the coordinate plane.
G.CO.A.2G.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.2G.CO.A.4G.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.1G.CO.A.4G.CO.C.9G.CO.D.12
Prove angle relationships in parallel line diagrams.
G.CO.A.1G.CO.C.9
Construct auxiliary parallel lines and use these in the development of proofs and identification of missing measures.
G.CO.C.9G.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.2G.CO.A.4G.CO.A.5G.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.2G.CO.A.5G.CO.B.6
Describe a sequence of rigid motions that will map a point, line segment, or angle onto another figure.
G.CO.A.5G.CO.B.6
Describe rigid motions, or sequences of rigid motions that have the same effect on a figure.
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