Triangle Congruence

Use rigid motions and valid triangle congruence criteria.

Lesson 5 of 53 parts Practice Flashcards

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Congruence via Rigid Motions

Objective: Explain congruence through a sequence of rigid motions.

Two figures are congruent if a sequence of rigid motions maps one exactly onto the other. Corresponding sides and angles are congruent.

Two triangles with matching tick marks on corresponding sides and a matching angle, showing congruence.

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Congruence via Rigid Motions

Objective: Explain congruence through a sequence of rigid motions.

Two figures are congruent if a sequence of rigid motions maps one exactly onto the other. Corresponding sides and angles are congruent.

Triangle Congruence Tests

Objective: Apply SSS, SAS, ASA, and AAS.

Triangles are congruent under SSS, SAS with included angle, ASA with included side, or AAS. Angle-angle-angle establishes similarity, not necessarily congruence.

Four triangles marked for SSS, SAS with the included angle, ASA with the included side, and AAS.

Ambiguity and Right-Triangle HL

Objective: Reject SSA generally and apply HL to right triangles.

SSA does not generally guarantee triangle congruence. For right triangles, equal hypotenuse and one corresponding leg imply congruence by HL.

Two right triangles with equal hypotenuses and one equal leg, which makes them congruent by HL.

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