Triangle Congruence Theorems

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What does ASA stand for in triangle congruence?

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ASA stands for Angle-Side-Angle, a theorem that states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

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What does AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a theorem that states if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

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What is the Angle-Angle (AA) criterion for triangle similarity?

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The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar, but not necessarily congruent.

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How can you prove triangles are congruent using the SSS theorem?

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

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How can you prove triangles are congruent using the SAS theorem?

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

Front

How can you prove triangles are congruent using the ASA theorem?

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To prove triangles are congruent using the ASA theorem, show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

How can you prove triangles are congruent using the AAS theorem?

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To prove triangles are congruent using the AAS theorem, show that two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.

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What is the significance of congruence in triangles?

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Congruence in triangles means that the triangles are identical in shape and size, allowing for the same measurements and properties.