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 SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a theorem stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a theorem stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, 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 stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, 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 stating that 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, 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 stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, 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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What is the significance of congruent triangles in geometry?

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Congruent triangles are significant because they allow for the establishment of equal lengths and angles, which is essential in proofs and constructions in geometry.

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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, measure all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

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

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