Triangle Congruence Theorems

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What does ASA stand for in triangle congruence?

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?

Back

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?

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 HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg, a theorem that applies to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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What is the SSA condition in triangle congruence?

Back

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

Front

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

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

Front

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

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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

What is the significance of the included angle in the SAS theorem?

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence in the SAS theorem.

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Can two triangles be congruent if only two sides are known?

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No, knowing only two sides (SSA) does not guarantee triangle congruence due to the possibility of different triangle configurations.