Triangle Congruency

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What is Triangle Congruency?

Back

Triangle congruency 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 congruency?

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

Front

What does SAS stand for in triangle congruency?

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SAS stands for Side-Angle-Side, a postulate 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 ASA stand for in triangle congruency?

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ASA stands for Angle-Side-Angle, a postulate 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.

Front

What does AAS stand for in triangle congruency?

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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 congruency?

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HL stands for Hypotenuse-Leg, a theorem that applies 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, then the triangles are congruent.

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What is the significance of the SSA condition in triangle congruency?

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SSA (Side-Side-Angle) does not guarantee triangle congruency because it can lead to ambiguous cases where two different triangles can be formed.

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How can you determine if two triangles are congruent using the SSS postulate?

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To determine if two triangles are congruent using the SSS postulate, measure all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

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What information is needed to prove triangles are congruent using the ASA postulate?

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To prove triangles are congruent using the ASA postulate, you need to know 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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Can two triangles be congruent if only one angle and two sides are known?

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No, knowing only one angle and two sides (SSA) does not guarantee congruency, as it can lead to different triangle configurations.