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 ASA stand for in triangle congruence?

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ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What does AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a criterion for triangle congruence where 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 does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are equal to the three sides of another triangle.

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What is the HL criterion in triangle congruence?

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HL stands for Hypotenuse-Leg, a criterion for triangle congruence applicable to right triangles, where the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle.

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If two triangles have two sides equal and the included angle equal, what can be concluded?

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The triangles are congruent by the SAS criterion.

Front

If two triangles have two angles equal, what can be concluded?

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The triangles are congruent by the AAS criterion.

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Can two triangles be congruent if only one side is equal?

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No, at least two sides and the included angle or two angles and a side must be equal for the triangles to be congruent.

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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 fundamental in proving other geometric properties and theorems.