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What does ASA stand for in triangle congruence?

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ASA stands for Angle-Side-Angle, a theorem used to prove that two triangles are congruent if 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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What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem used to prove that two triangles are congruent 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.

Front

What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a theorem used to prove that two triangles are congruent if 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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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a theorem used to prove that two triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.

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What does HL stand for in triangle congruence?

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

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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 method for proving triangle congruence because it can lead to ambiguous cases.

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What is the significance of congruent triangles in geometry?

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Congruent triangles have the same size and shape, meaning their corresponding sides and angles are equal, which is fundamental in proving other geometric properties.

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

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To use the AAS theorem, 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 difference between ASA and AAS?

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ASA requires the included side between two angles to be equal, while AAS does not require the side to be included between the two angles.

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Can two triangles be congruent if only one side is known?

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No, knowing only one side is not sufficient to prove triangle congruence; at least two sides and the included angle or two angles and a side are needed.