Curriculum  /  Math  /  10th Grade  /  Unit 2: Congruence in Two Dimensions  /  Lesson 7

Congruence in Two Dimensions

Lesson 7

Math

Unit 2

10th Grade

Lesson 7 of 18

Objective

Describe a sequence of rigid motions that map a pre-image to an image (specifically triangles, rectangles, parallelograms, and regular polygons).

Common Core Standards

Core Standards

  • 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.6 — Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Foundational Standards

  • 8.G.A.2

Criteria for Success

  1. Distinguish correspondence from congruence and determine when a correspondence is also congruent. 
  2. Predict transformations necessary to map one figure onto another.
  3. Verify the sequence of transformations experimentally using patty paper.
  4. Describe the sequence of transformations on a coordinate plane required to map one figure onto another. 
  5. Describe the sequence of transformations off the coordinate plane required to map one figure onto another. 
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Anchor Problems

25-30 minutes

Problem 1

Describe a sequence of transformations that will map Figure A to Figure B

.

Guiding Questions

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Problem 2

What sequence of transformations will map Figure 1 to Figure 3?

Guiding Questions

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Target Task

5-10 minutes

A rectangle has coordinate points at $${A(1,0)}$$, $${B(1,4)}$$, $${C(3,0)}$$,and $${D(3,4)}$$.

What sequence of transformations would result in rectangle with coordinate points at 

$${A''(-3,1)}$$, $${B''(1,1)}$$, $${C''(1,3)}$$, and $${D''(-3,3)}$$? 

  1. Show the figures on a coordinate plane. 
  2. Describe a sequence of transformations. 
  3. Show the transformation of one point using algebraic rules to show your transformations make sense.

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 where a sequence of transformations is given and students need to match to the appropriate graph or diagram.

Next

Describe single rigid motions, or sequences of rigid motions that have the same effect on a figure.

Lesson 8
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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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