Congruence in Two Dimensions

Lesson 12

Math

Unit 2

10th Grade

Lesson 12 of 18

Objective


Develop Angle, Side, Angle (ASA) and Side, Side, Side (SSS) congruence criteria. Describe how the criteria develop from rigid motions.

Common Core Standards


Core Standards

  • 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.
  • G.CO.B.8 — Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Foundational Standards

  • 7.G.A.2
  • 8.G.A.2

Criteria for Success


  1. Identify the criteria necessary to create a unique triangle, given congruent sides, angles and their relative positions. 
  2. Describe how just knowing the number of congruent sides and angles is not enough to establish congruence, the relative position is important to determine congruence (distinguish SSA from SAS).
  3. Use properties of transformations of angle and distance preservation as evidence for ASA and SSS. 
  4. Identify SSS as a congruence criteria and relate to the triangle inequality theorem. 

Tips for Teachers


Straws, Cuisenaire rods are helpful to have students experiment with making a triangle. You do not need to have the same length for each person, and only three lengths are needed for each person to form a triangle.

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Anchor Problems

25-30 minutes


Problem 1

Choose two lengths. Create more than one triangle.

Guiding Questions

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Problem 2

What theorem is this video suggesting?

How can we determine if it's true?

Guiding Questions

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References

101Questions Triangles

Triangles by Andrew Stadel is made available on 101Questions under the CC BY 3.0 license. Accessed Aug. 10, 2017, 1:40 p.m..

Target Task

5-10 minutes


Given: $${BD=CD}$$$$C$$ is the midpoint of $${\overline{AB}}$$.

A: Prove that triangle $$ACD$$ is congruent to triangle $$BCD$$ using SSS.

B: Prove that triangle $$ACE$$ is congruent to triangle $$BCE$$ using SAS in TWO WAYS.

References

EngageNY Mathematics Geometry > Module 1 > Topic D > Lesson 24

Geometry > Module 1 > Topic D > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

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 “What is the only possible point for vertex $$C$$ of triangle $$ABC$$? Given: $$B$$ and $$D$$ are collinear, $$A$$ and $$E$$ are collinear. Show your reasoning algebraically.” 

  • EngageNY Mathematics Geometry > Module 1 > Topic D > Lesson 24
  • New Visions for Public Schools Unit 2 Big Idea 3"Finding Sides in Triangles #1" from Instructional Routine: Contemplate then Calculate
  • MARS Formative Assessment Lessons for Grade 7 Describing and Defining TrianglesThis is a 7th grade lesson, but is highly applicable to the material in this lesson. Be sure to ask course level appropriate questions.
  • New Visions for Public Schools Unit 2 Big Idea 3"Finding Sides in Triangles #3" from Instructional Routine: Contemplate then Calculate

Next

Use triangle congruence criteria, rigid motions, and other properties of lines and angles to prove congruence between different triangles.

Lesson 13
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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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