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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 does the acronym ASA stand for in triangle congruence?

Back

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 the acronym 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 is the HL theorem in triangle congruence?

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HL stands for Hypotenuse-Leg, a theorem that states if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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Can two triangles be congruent if only two angles are known?

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No, knowing only two angles does not guarantee congruence; the third angle can vary, leading to different triangle sizes.

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What is the significance of the included angle in the SAS theorem?

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The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence in the SAS theorem.

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

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To prove congruence using AAS, show that 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 is the difference between ASA and AAS?

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ASA requires the included side between two angles to be equal, while AAS allows for a non-included side to be equal.

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What is a necessary condition for using the SSS theorem?

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All three sides of one triangle must be equal to all three sides of another triangle.