Congruence in Two Dimensions

Lesson 13

Math

Unit 2

10th Grade

Lesson 13 of 18

Objective


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

Common Core Standards


Core Standards

  • G.SRT.B.5 — Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Foundational Standards

  • 7.G.A.2
  • 8.G.A.2

Criteria for Success


  1. Annotate a diagram with all congruent relationships using appropriate notation. 
  2. Develop a series of statements and evidence that prove that two triangles are congruent by the SAS, ASA, and SSS criteria. 
  3. Identify and develop proofs when the SAS, SSS, and ASA criteria are met in diagrams where triangles are embedded.
  4. Identify missing measures directly and algebraically in triangles where the SAS, ASA, and SSS criteria are met. 
  5. Identify errors in proof where the SAS, ASA, and SSS criteria are not met, but used in arguments. Correct reasoning.
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Anchor Problems


Problem 1

Given: $${\angle1 \cong \angle2, \overline{RM} \cong \overline{TM}}$$

Prove: $${\overline{SM}}$$ bisects $${\angle RST}$$

Guiding Questions

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Problem 2

Given: $${m\angle A=m\angle D, AB = DC}$$

Prove: $${\triangle CAB \cong \triangle BDC}$$

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 1 > Topic D > Lesson 24Exercise 4

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..

Target Task


Prove that triangle SKT and triangle RLT are congruent. Describe the given, describe what you are proving, and show how you would use transformations and triangle congruence criteria in your proof.

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 that ask students to construct isosceles triangles by copying base angles.
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Lesson 12

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Lesson 14

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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