Congruence in Two Dimensions

Lesson 1

Math

Unit 2

10th Grade

Lesson 1 of 18

Objective


Define polygon and identify properties of polygons.

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Define a polygon as a closed figure. 
  2. Distinguish between convex polygons (all interior angles less than 180°), and concave polygons (one or more interior angles as greater than 180°). 
  3. Describe the features of polygons and classify on the basis of the features of a polygon: 
    1. Number of sides/angles 
    2. Relative length of sides 
    3. Parallel or perpendicular sides 
    4. Presence of right angles 
    5. Presence of interior angles that are less or greater than 180°
  4. Determine the least amount of description necessary to accurately classify polygons and identify features that discriminate one polygon from another. 

Tips for Teachers


  • This lesson prepares students to access standard G-CO.3, but has a focus on elementary standards for review.  
  • The inclusive definition of trapezoids is used throughout this lesson. Trapezoids are quadrilaterals that contain at least one pair of parallel sides.
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Anchor Problems

25-30 minutes


Problem 1

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?

Guiding Questions

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Problem 2

Without looking at any resources, define the following terms concisely and accurately.  

  • Polygon
  • Parallelogram
  • Triangle

Guiding Questions

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References

Continuous Everywhere But Differentiable Nowhere Attacks and Counterattacks in Geometry

Problem 3

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. 

  1. A rhombus is a square
  2. A triangle is a parallelogram
  3. A square is a parallelogram
  4. A square is a rhombus
  5. A parallelogram is a rectangle
  6. A trapezoid is a parallelogram
  7. A trapezoid is a quadrilateral

Guiding Questions

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References

Illustrative Mathematics Always, Sometimes, Never

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.

Modified by Fishtank Learning, Inc.

Target Task

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?

Additional Practice


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.

Next

Prove interior and exterior angle relationships in triangles.

Lesson 2
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to Polygons

Topic B: Rigid Motion Congruence of Two-Dimensional Figures

Topic C: Triangle Congruence

Topic D: Parallelogram Properties from Triangle Congruence

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