Congruence in Two Dimensions

Lesson 10

Math

Unit 2

10th Grade

Lesson 10 of 18

Objective


Prove angle relationships using the Side Angle Side criteria.

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

  • 8.G.A.2
  • 8.G.A.5

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 criteria. 
  3. Identify and develop proofs when the SAS criteria is met in diagrams where triangles are embedded.
  4. Identify missing measures directly and algebraically in triangles where the SAS criteria is met. 
  5. Identify errors in proof where the SAS criteria is not met, but used in arguments.
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Anchor Problems


Problem 1

Given: $${\overline{AB} \parallel \overline{CD}}$$ and $${\overline{AB} \cong \overline{CD}}$$

Prove: $${\triangle ABD \cong \triangle CDB}$$

Guiding Questions

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Problem 2

Prove that  $${\triangle BEC \cong \triangle ADC}$$ given that $$C$$ is the midpoint of $${\overline{DE}}$$ and $${\overline {AB}}$$

Guiding Questions

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Problem 3

The proof below is incorrect. Identify the statement and reason that are incorrect, and correct the reasoning. 
Given: $${\overline{BD} \cong \overline{EC}}$$, $${\overline {BA} \cong \overline{EA}}$$$${\angle BCE \cong \angle EDB}$$.
Prove: $${\triangle ABD \cong \triangle AEC}$$

Guiding Questions

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Target Task


Given: $${AC \perp BC}$$, $$D$$ is the midpoint of $${\overline{AC}}$$

Prove: $$\triangle ABC \cong \triangle CBD$$

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.

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Lesson 9

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Lesson 11

Lesson Map

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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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