Triangle Congruence Theorems

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

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To prove triangles are congruent using SAS, show that two sides of one triangle are equal to two sides of another triangle and that the angle between those sides is equal.

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

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To prove triangles are congruent using ASA, show that two angles of one triangle are equal to two angles of another triangle and that the side between those angles is equal.

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

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To prove triangles are congruent using AAS, show that two angles of one triangle are equal to two angles of another triangle and that a non-included side is equal.

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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, show that all three sides of one triangle are equal to all three sides of another triangle.

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What is the significance of triangle congruence theorems?

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Triangle congruence theorems are significant because they provide criteria to determine if two triangles are identical in shape and size, which is essential in geometry.