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 SAS stand for in triangle congruence?

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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 the acronym AAS stand for in triangle congruence?

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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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What is the SSS theorem in triangle congruence?

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SSS stands for Side-Side-Side, a theorem that states 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 ASA theorem in triangle congruence?

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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 is the HL theorem in triangle congruence?

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HL stands for Hypotenuse-Leg, a theorem applicable to right triangles that states 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 does SSA stand for in triangle congruence?

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

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How can you determine if two triangles are congruent using the SSS theorem?

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To determine if two triangles are congruent using the SSS theorem, measure all three sides of both triangles. If all corresponding sides are equal, the triangles are congruent.

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What is the significance of corresponding parts in triangle congruence?

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Corresponding parts refer to the sides and angles of two triangles that are matched based on their congruence. If two triangles are congruent, their corresponding parts are equal.

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What is the relationship between triangle congruence and similarity?

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Triangle congruence means that triangles are the same size and shape, while similarity means that triangles have the same shape but may differ in size.