Triangle Congruence Theorems

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a theorem stating that if three sides of one triangle are equal to three sides of another triangle, 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 stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, 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 stating that 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, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

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

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What is the difference between SSA and other triangle congruence theorems?

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SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

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How can you prove triangles are congruent using SSS?

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To prove triangles are congruent using SSS, show that all three corresponding sides of the triangles are equal in length.

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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 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.

Front

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 corresponding included side of another triangle.

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What is the importance of triangle congruence theorems in geometry?

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Triangle congruence theorems are important because they provide methods to prove that two triangles are identical in shape and size, which is fundamental in solving geometric problems.