SSS and SAS Proofs

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What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are equal to the three sides of another triangle.

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What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

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What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning ∆ABC ≅ ∆ABC.

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What is the Transitive Property in geometry?

Back

The Transitive Property states that if one figure is congruent to a second figure, and the second figure is congruent to a third figure, then the first figure is congruent to the third figure.

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What is ASA in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

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What is AAS in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

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What is HL in triangle congruence?

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HL stands for Hypotenuse-Leg, a criterion for triangle congruence applicable to right triangles, where the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle.

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What is the significance of congruent triangles?

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Congruent triangles have the same size and shape, meaning all corresponding sides and angles are equal, which is crucial in proving geometric properties.

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How do you prove triangles are congruent using SSS?

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To prove triangles are congruent using SSS, show that all three sides of one triangle are equal to the three sides of another triangle.

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How do you prove triangles are congruent using SAS?

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To prove triangles are congruent using SAS, show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.