Curriculum  /  Math  /  10th Grade  /  Unit 2: Congruence in Two Dimensions  /  Lesson 4

Congruence in Two Dimensions

Lesson 4

Math

Unit 2

10th Grade

Lesson 4 of 18

Objective

Determine congruence of two dimensional figures by translation.

Common Core Standards

Core Standards

  • G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
  • G.CO.A.4 — Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • G.CO.A.5 — Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
  • G.CO.B.7 — Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Foundational Standards

  • 8.G.A.1
  • 8.G.A.2
  • 8.G.A.3

Criteria for Success

  1. Describe how translation of points and line segments can be extended to translate polygonal figures.
  2. Translate polygons described by algebraic rules (specifically triangles, rectangles, parallelograms, and regular polygons) on the coordinate plane. 
  3. Translate polygons described by vectors (specifically triangles, rectangles, parallelograms, and regular polygons) off the coordinate plane using constructions and patty paper. 
  4. Determine whether two polygons are congruent through transformation by translation. 
  5. Describe why two polygons are congruent and highlight the angle and distance preservation of translations as evidence.
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Anchor Problems

25-30 minutes

Problem 1

Below are four original points, and four points after transformation.

Are polygon $${ABCD}$$ and polygon $${A'B'C'D'}$$ congruent? Explain your reasoning.

Guiding Questions

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Problem 2

Allison says that the following two figures are congruent because they have the “same size, same shape”. Describe why her reasoning is incorrect, using the properties of translation as evidence.

Guiding Questions

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Target Task

5-10 minutes

Create a congruent figure to the one shown in the diagram below.

  • Identify the translation rule you used for the figure.  
  • Describe how you know the figures are congruent using properties of translations. 

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.

  • Include problems such as: 
    • Trace figure on patty paper and translate according to an algebraic rule. 
    • Given a transformation, identify algebraic rule. 
    • Translate one point of a geometric figure; identify the rest of the figure and the algebraic rule. 
    • Identification of reflection, rotation, and translation. 
    • Question about relationship between line segments of translated figure. (Draw a line between corresponding points between translated figures.) What is the relationship between all of the lines drawn?

Next

Reflect two dimensional figures on and off the coordinate plane.

Lesson 5
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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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