Triangle Congruence

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What is Triangle Congruence?

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Triangle Congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

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What does 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 SSS stand for 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 does ASA stand for 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 does 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 does HL stand for 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 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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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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How can you determine if two triangles are congruent using the SAS theorem?

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To determine if two triangles are congruent using the SAS theorem, measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, the triangles are congruent.

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What is the significance of congruent triangles in geometry?

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Congruent triangles are significant in geometry because they allow for the establishment of equal lengths and angles, which can be used in proofs and problem-solving.