Triangle Congruence

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What is Triangle Congruence?

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Triangle congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

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What does the acronym ASA stand for in triangle congruence?

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ASA stands for Angle-Side-Angle, a rule 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 the acronym AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a rule 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.

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What does the acronym SSS stand for in triangle congruence?

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

Front

What does the acronym SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a rule 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 is the significance of corresponding angles in triangle congruence?

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Corresponding angles are angles in two triangles that occupy the same relative position. If two triangles are congruent, their corresponding angles are equal.

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What is the significance of corresponding sides in triangle congruence?

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Corresponding sides are sides in two triangles that are in the same relative position. If two triangles are congruent, their corresponding sides are equal in length.

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Can two triangles be congruent if only one angle and one side are known?

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No, knowing only one angle and one side (SSA) does not guarantee triangle congruence, as it can lead to ambiguous cases.

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What is the criteria for triangle congruence using the SSS rule?

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For the SSS rule, if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

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What is the criteria for triangle congruence using the SAS rule?

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For the SAS rule, 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.