Standard #: MAFS.912.G-CO.2.8 (Archived Standard)


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Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Understand congruence in terms of rigid motions. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Assessed with:
    MAFS.912.G-CO.2.6



Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

Triangles BKW and DMT are shown where angle B approximately equal to angle D comma space angle K approximately equal to angle T comma space stack B K with bar on topapproximately equal to stack D T with bar on top

This question has three parts.

Rashhaad performs a sequence of transformations on begin mathsize 12px style increment B K W end style to map it to begin mathsize 12px style increment D T M end style.

Part A. Which sequence of transformations could be used to map begin mathsize 12px style increment B K W end style to begin mathsize 12px style increment D T M end style?

Part B. The coordinate grid below shows three triangles that could be an intermediate step of Rashaad's sequence of transformations.

Step 1: Use the Add Arrow tool to map the vertices of begin mathsize 12px style increment B K W end style to show the translation (s) chosen in part A.

Step 2: Then, label the transformed triangle by dragging B',K', and W' to the correct vertex.

Part C.

Rashaad wants to justify that angle B approximately equal to angle D comma space angle K approximately equal to angle T comma space stack B K with bar on topapproximately equal to stack D T with bar on top are sufficient to show that the triangles are congruent.

Select words, phrases or equations to complete Rashaad's justification.

 N/A : Multiple Types


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Related Resources

Formative Assessments

Name Description
Justifying HL Congruence

Students are asked to use rigid motion to explain why the HL pattern of congruence ensures right triangle congruence.

Justifying SSS Congruence

Students are asked to use rigid motion to explain why the SSS pattern of congruence ensures triangle congruence.

Justifying SAS Congruence

Students are asked to use rigid motion to explain why the SAS pattern of congruence ensures triangle congruence.

Justifying ASA Congruence

Students are asked to use rigid motion to explain why the ASA pattern of congruence ensures triangle congruence.

Lesson Plans

Name Description
Turning to Congruence

This lesson uses rigid motions to prove the ASA and HL triangle congruence theorems.

Analyzing Congruence Proofs

Students work on the concept of congruency whilst developing their understanding of proof in a geometric context. This lesson is intended to help students learn to:

  • Work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles.
  • Identify and understand the significance of a counterexample.
  • Prove, and evaluate proofs in a geometric context.

Problem-Solving Tasks

Name Description
Why Does ASA Work?

This problem solving task ask students to show the reflection of one triangle maps to another triangle.

When Does SSA Work to Determine Triangle Congruence?

In this problem, we considered SSA. The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence.

Why Does SAS Work?

This problem solving task challenges students to explain the reason why the given triangles are congruent, and to construct reflections of the points.

Why does SSS work?

This particular problem solving task exhibits congruency between two triangles, demonstrating translation, reflection and rotation.

Are the Triangles Congruent?

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Tutorials

Name Description
Finding congruent triangles

In this tutorial, students will use the SSS, ASA, SAS, and AAS postulates to find congruent triangles

Using SSS in a proof

This tutorial discusses the difference between a theorem and axiom. It also shows how to use SSS in a proof.

Triangle congruence postulates

This tutorial discusses SSS, SAS, ASA and AAS postulates for congruent triangles. It also shows AAA is only good for similarity and SSA is good for neither.

Congruent Triangles and SSS

In this video, students will learn about congruent triangles and the "Side-Side-Side" postulate.

Worksheet

Name Description
Congruence of Quadrilaterals

Students are provided two pairs of quadrilaterals with information that relates those in each of the pairs. The objective is to prove that each of the pairs are congruent. The teacher will provide guidance to the students as necessary by suggesting a triangle congruence theorem and/or construction of a diagonal.

Student Resources

Problem-Solving Tasks

Name Description
Why Does ASA Work?:

This problem solving task ask students to show the reflection of one triangle maps to another triangle.

When Does SSA Work to Determine Triangle Congruence?:

In this problem, we considered SSA. The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence.

Why Does SAS Work?:

This problem solving task challenges students to explain the reason why the given triangles are congruent, and to construct reflections of the points.

Why does SSS work?:

This particular problem solving task exhibits congruency between two triangles, demonstrating translation, reflection and rotation.

Are the Triangles Congruent?:

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Tutorials

Name Description
Finding congruent triangles:

In this tutorial, students will use the SSS, ASA, SAS, and AAS postulates to find congruent triangles

Using SSS in a proof:

This tutorial discusses the difference between a theorem and axiom. It also shows how to use SSS in a proof.

Triangle congruence postulates:

This tutorial discusses SSS, SAS, ASA and AAS postulates for congruent triangles. It also shows AAA is only good for similarity and SSA is good for neither.

Congruent Triangles and SSS:

In this video, students will learn about congruent triangles and the "Side-Side-Side" postulate.



Parent Resources

Problem-Solving Tasks

Name Description
Why Does ASA Work?:

This problem solving task ask students to show the reflection of one triangle maps to another triangle.

When Does SSA Work to Determine Triangle Congruence?:

In this problem, we considered SSA. The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence.

Why Does SAS Work?:

This problem solving task challenges students to explain the reason why the given triangles are congruent, and to construct reflections of the points.

Why does SSS work?:

This particular problem solving task exhibits congruency between two triangles, demonstrating translation, reflection and rotation.

Are the Triangles Congruent?:

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.



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