G-CO.2.8

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

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Students are asked to use rigid motion to explain why the ASA pattern of congruence ensures triangle congruence.
Justifying ASA Congruence
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Students are asked to use rigid motion to explain why the SAS pattern of congruence ensures triangle congruence.
Justifying SAS Congruence
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Students are asked to use rigid motion to explain why the HL pattern of congruence ensures right triangle congruence.
Justifying HL Congruence
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For these particular triangles, three reflections were necessary to express how to move from ABC to DEF. Sometimes, however, one reflection or two reflections will suffice.
Why Does SAS work?
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The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information.
When Does SSA Work to Determine Triangle Congruence?
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This particular sequence of transformations which exhibits a congruency between triangles ABC and DEF used one translation, one rotation, and one reflection.
Why Does SSS work?
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The goal of this task is to establish the SSS congruence criterion using rigid motions.
SSS Congruence Criterion
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Unlike the SAS criterion for congruence, where it can be vital that the congruent angles be the ones determined by the corresponding sides, the ASA criterion for congruence works equally well for any two angles.
Why Does ASA Work?