Curriculum  /  Math  /  10th Grade  /  Unit 2: Congruence in Two Dimensions  /  Lesson 8

Congruence in Two Dimensions

Lesson 8

Math

Unit 2

10th Grade

Lesson 8 of 18

Objective

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

Common Core Standards

Core Standards

  • G.CO.A.3 — Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • 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. Describe how reflections/rotations of 180 degrees are related and translations/reflections are related when line segments are parallel to a line of reflection. 
  2. Relate the rotational symmetry of a figure to the reflectional symmetry of a figure and describe how the congruence of these two rigid motions applies to both reflectional and rotational symmetry. 
  3. Describe the features of a figure where some rigid motions have the same effect and some do not (ie: angles and line segments may not have the same set of congruent rigid motions). 
  4. Explain the characteristics of each transformation in the sequence that mimic a single transformation.
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Anchor Problems

25-30 minutes

Problem 1

Describe whether the following statement is always, sometimes, or never true:
“If you reflect a figure across two parallel lines, the result can be described with a single translation rule.”

Guiding Questions

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Problem 2

Describe whether the following statement is always, sometimes, or never true: 
“The reflection of a figure over two unique lines of reflection can be described by a rotation.”

Guiding Questions

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Problem 3

Johnny says three rotations of $${90^{\circ}}$$ about the center of the figure is the same as three reflections with lines that pass through the center, so a figure with order 4 rotational symmetry results in a figure that also has reflectional symmetry.  

Describe, using evidence from the two drawings below, to support or refute Johnny’s statement.

Guiding Questions

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Target Task

5-10 minutes

Describe whether the converse of the statement in Anchor Problem #2 is always, sometimes, or never true:

Converse: “The rotation of a figure can be described by a reflection of a figure over two unique lines of reflection.”

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.

  • Independent practice for this lesson will ensure that the criteria for sequences of transformations and parameters for transformations are met.

Next

Develop the Side Angle Side criteria for congruent triangles through rigid motions.

Lesson 9
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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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