Triangle Congruence

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What is Triangle Congruence?

Back

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 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 SAS stand for in triangle congruence?

Back

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.

Front

What does SSS stand for in triangle congruence?

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

Front

What does 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 is the Hypotenuse-Leg (HL) theorem?

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The Hypotenuse-Leg theorem states that 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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If ∆ABC ≅ ∆XYZ, what can be concluded about their corresponding sides?

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If ∆ABC ≅ ∆XYZ, then AB ≅ XY, BC ≅ YZ, and AC ≅ XZ.

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What is the significance of congruence in triangles?

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Congruence in triangles is significant because it allows us to determine that two triangles are identical in shape and size, which is essential in solving geometric problems.

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How can you prove two triangles are congruent using the ASA postulate?

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To prove two triangles are congruent using the ASA postulate, show that 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 is the relationship between corresponding angles in congruent triangles?

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In congruent triangles, corresponding angles are equal.