Congruence in Two Dimensions

Lesson 14

Math

Unit 2

10th Grade

Lesson 14 of 18

Objective


Prove triangles congruent using Angle, Angle, Side (AAS), and describe why AAA is not a congruency criteria.

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.
  • G.CO.C.10 — Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Foundational Standards

  • 7.G.A.2
  • 8.G.A.2

Criteria for Success


  1. Describe how AAS follows from the ASA criteria. 
  2. Identify triangles with three congruent angles and describe why these triangles are not congruent.
  3. Generalize that if you know two angles and one side (regardless of position) that the triangles are congruent. 
  4. Identify when, in proofs, the AAS criteria can be used to establish relationships.
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Anchor Problems

25-30 minutes


Problem 1

Are the following triangles congruent?

Guiding Questions

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Problem 2

Are all of the following triangles congruent?

Guiding Questions

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Target Task

5-10 minutes


Given: $${\overline{CB} \cong \overline{DE}, \overline{AC} \cong \overline{AD}, \angle FCB \cong \angle FDE}$$

Prove: $${\overline{BD} \cong \overline{EC}}$$

References

EngageNY Mathematics Geometry > Module 1 > Topic D > Lesson 25Exit Ticket

Geometry > Module 1 > Topic D > Lesson 25 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..

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.

Next

Develop the Hypotenuse- Leg (HL) criteria, and describe the features of a triangle that are necessary to use the HL criteria.

Lesson 15
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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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