Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 3
Math
Unit 2
10th Grade
Lesson 3 of 18
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Lesson Notes
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Describe and apply the sum of interior and exterior angles of polygons.
The core standards covered in this lesson
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.
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
Suggestions for teachers to help them teach this lesson
This lesson has been written to meet the Massachusetts standard of G-CO.11a, specifically addressing interior and exterior angles. The Common Core standard G-CO.11 does not specifically call out interior and exterior angles.
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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
Which of the following figures has the largest sum of interior angles?
Recipes for Surprising Mathematics by Dan Meyer is made available at dy/dan under the CC BY 4.0 license. Accessed March 8, 2017, 11:47 a.m..
Which of the following has the greatest sum of exterior angles?
Angles in Polygons Problems - Items - Tasks by Jennifer Wilson is made available on Easing the Hurry Syndrome. Accessed Aug. 10, 2017, 10:02 a.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Compare the quantity in Column A with the quantity in Column B.
Geometry Resources by Standard is made available on JMAP by Steve Sibol and Steve Watson. Copyright © 2017 JMAP, Inc. - All rights reserved. Accessed Aug. 10, 2017, 10:07 a.m..
Find the measure of an interior angle and an exterior angle of a regular polygon with 40 sides.
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.
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Determine congruence of two dimensional figures by translation.
Topic A: Introduction to Polygons
Define polygon and identify properties of polygons.
Standards
G.CO.A.1G.CO.C.11
Prove interior and exterior angle relationships in triangles.
G.CO.C.10
G.CO.C.11
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Topic B: Rigid Motion Congruence of Two-Dimensional Figures
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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