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.

Front

What does SAS stand for in triangle congruence?

Back

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 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.

Front

What does AAS stand for in triangle congruence?

Back

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 the corresponding non-included side of another triangle, then the triangles are congruent.

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What is the SSA condition in triangle congruence?

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SSA stands for Side-Side-Angle, which is not a valid condition for proving triangle congruence because it can lead to ambiguous cases.

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How can you prove triangles are congruent using ASA?

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To prove triangles are congruent using ASA, show that 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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How can 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.

Front

How can 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 all three sides of another triangle.

Front

How can you prove triangles are congruent using AAS?

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To prove triangles are congruent using AAS, show that 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 the significance of triangle congruence theorems?

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Triangle congruence theorems are significant because they provide criteria to determine if two triangles are identical in shape and size, which is essential in geometry.