Curriculum / Math / 10th Grade / Unit 1: Constructions, Proof, and Rigid Motion / Lesson 12
Math
Unit 1
10th Grade
Lesson 12 of 19
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Prove angle relationships in parallel line diagrams.
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.C.9 — Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
The foundational standards covered in this lesson
8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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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
Find all the angle measures that equal 127° and all the angle measures that are supplementary to 127°.
In the figure, $${\overline{AB} \parallel \overline{CD}}$$ and $${\overline{EF} \parallel \overline{GH}}$$. Prove that $${\angle AFE \cong \angle DKH}$$.
Geometry > Module 1 > Topic C > Lesson 18 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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5-10 minutes
$${\overline{AD} \parallel \overline{BC}}$$ and $${\angle EJB}$$ is supplementary to $${\angle JBK}$$. Prove that $${\overline {AD} \parallel \overline{JE}}$$.
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Construct auxiliary parallel lines and use these in the development of proofs and identification of missing measures.
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
Construct a perpendicular bisector.
Construct the altitudes and perpendicular bisectors of sides of triangles.
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
G.CO.A.1G.CO.C.9
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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