Curriculum  /  Math  /  10th Grade  /  Unit 2: Congruence in Two Dimensions  /  Lesson 5

Congruence in Two Dimensions

Lesson 5

Math

Unit 2

10th Grade

Lesson 5 of 18

Objective

Reflect two dimensional figures on and off the coordinate plane.

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.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.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. Reflect polygons described by algebraic rules (specifically triangles, rectangles, parallelograms, and regular polygons) on the coordinate plane. 
  2. Reflect polygons by description (specifically triangles, rectangles, parallelograms, and regular polygons) off the coordinate plane using constructions and patty paper. 
  3. Determine whether two polygons (specifically triangles) are congruent through transformation by reflection. 
  4. Describe why two polygons are congruent and highlight the angle and distance preservation of reflections as evidence. 
  5. Given a line of reflection that is also a line of symmetry, describe why the polygon will map onto itself. 
  6. Identify all lines of reflectional symmetry and verify that the polygon maps onto itself.
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Anchor Problems

25-30 minutes

Problem 1

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

Are $${\triangle ABC}$$ and $${\triangle A'B'C'}$$ congruent? Explain your reasoning.

Guiding Questions

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Problem 2

Below is rectangle $${ABCD}$$. 

Identify a line of reflection so that the rectangle maps onto itself.

Guiding Questions

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Problem 3

Describe how you know that the two figures are congruent using a sequence of translation and reflection.

Guiding Questions

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Target Task

5-10 minutes

Draw a triangle that has one line of reflection on the coordinate plane below.

Describe the properties of reflections that support your reasoning.

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 the lines of reflection of regular polygons are compared to the lines of reflection of irregular polygons (ie: square vs. rectangle/rhombus). Describe which regular polygons have the same number of lines of reflection as the number of sides.

Next

Rotate two dimensional figures on and off the coordinate plane.

Lesson 6
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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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