Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 1
Math
Unit 2
10th Grade
Lesson 1 of 18
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Define polygon and identify properties of polygons.
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.11 — Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
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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
Your friend gives you a bunch of shapes and asks you to choose one, but not tell him or her. Choose a figure. What are the features of this polygon that set it apart from the rest of the polygons shown?
Without looking at any resources, define the following terms concisely and accurately.
Decide whether each of these statements is always, sometimes, or never true. If it is sometimes true, draw and describe a figure for which the statement is true and another figure for which the statement is not true.
Always, Sometimes, Never, accessed on March 8, 2017, 11:39 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A convex polygon with one pair of parallel sides can be generally classified as a trapezoid. What would need to be true about this shape to also be classified as a rhombus?
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Prove interior and exterior angle relationships in triangles.
Topic A: Introduction to Polygons
Standards
G.CO.A.1G.CO.C.11
G.CO.C.10
Describe and apply the sum of interior and exterior angles of polygons.
G.CO.C.11
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Topic B: Rigid Motion Congruence of Two-Dimensional Figures
Determine congruence of two dimensional figures by translation.
G.CO.A.2G.CO.A.4G.CO.A.5G.CO.B.7
Reflect two dimensional figures on and off the coordinate plane.
G.CO.A.2G.CO.A.3G.CO.A.5G.CO.B.7
Rotate two dimensional figures on and off the coordinate plane.
Describe a sequence of rigid motions that map a pre-image to an image (specifically triangles, rectangles, parallelograms, and regular polygons).
G.CO.A.5G.CO.B.6
Describe single rigid motions, or sequences of rigid motions that have the same effect on a figure.
G.CO.A.3G.CO.A.5G.CO.B.6
Topic C: Triangle Congruence
Develop the Side Angle Side criteria for congruent triangles through rigid motions.
G.CO.B.7G.CO.B.8
Prove angle relationships using the Side Angle Side criteria.
G.SRT.B.5
Prove and apply that the points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
G.CO.A.2G.CO.C.10G.CO.C.9
Develop Angle, Side, Angle (ASA) and Side, Side, Side (SSS) congruence criteria. Describe how the criteria develop from rigid motions.
Use triangle congruence criteria, rigid motions, and other properties of lines and angles to prove congruence between different triangles.
Prove triangles congruent using Angle, Angle, Side (AAS), and describe why AAA is not a congruency criteria.
G.CO.B.7G.CO.B.8G.CO.C.10
Develop the Hypotenuse- Leg (HL) criteria, and describe the features of a triangle that are necessary to use the HL criteria.
G.CO.B.7G.CO.C.10
Use criteria for triangle congruence to prove relationships among angles and sides in geometric problems.
G.CO.C.9G.SRT.B.5
Topic D: Parallelogram Properties from Triangle Congruence
Prove that the opposite sides and opposite angles of a parallelogram are congruent.
Prove theorems about the diagonals of parallelograms.
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