Triangle Congruence Theorems

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What does ASA stand for in triangle congruence theorems?

Back

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 SSS stand for in triangle congruence theorems?

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

Front

What does SAS stand for in triangle congruence theorems?

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.

Front

What does AAS stand for in triangle congruence theorems?

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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Can SSA be used to prove triangle congruence?

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No, SSA (Side-Side-Angle) cannot be used to prove triangle congruence as it does not guarantee that the triangles are congruent.

Front

If two triangles have two angles equal, what can be said about their sides?

Back

If two triangles have two angles equal, the third angle will also be equal, and the triangles are similar, but not necessarily congruent unless the sides are also proportional.

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What is the relationship between congruent triangles and their corresponding parts?

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In congruent triangles, all corresponding sides and angles are equal.

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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 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.

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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.