Curriculum / Math / 10th Grade / Unit 1: Constructions, Proof, and Rigid Motion / Lesson 2
Math
Unit 1
10th Grade
Lesson 2 of 19
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Construct an equilateral triangle with only a straight-edge and a compass. Copy a line segment.
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.
G.CO.D.13 — Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
The foundational standards covered in this lesson
7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students will need compasses and straight edges for this lesson.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
All the circles below have congruent radii, but different centers.
Margi has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her calico cat? Use the scale drawing of Margie’s room shown below, together with (only) a compass and straight edge. Place an M where Mack will be if the theory is true.
Geometry > Module 1 > Topic A > Lesson 1 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..
The cats changed positions. Mack left the room. Simon and JoJo also moved but stayed the same distance apart. Draw two new locations for Simon and JoJo.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Below is an equilateral triangle. Show the constructions that could have been used to create this equilateral triangle.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 1
Lesson 3
Topic A: Constructions of Basic Geometric Figures
Describe the precise definition and notation for foundational geometric figures.
G.CO.A.1
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
Describe rigid motions. Use algebraic rules to translate points and line segments and describe translations on the coordinate plane.
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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