Triangle Congruence

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What is Triangle Congruence?

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Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

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What does the H-L Theorem state?

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The H-L Theorem (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 two triangles are congruent.

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What is the AAS Congruence Postulate?

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The AAS (Angle-Angle-Side) Congruence Postulate states that if two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent.

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What is the SAS Congruence Postulate?

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The SAS (Side-Angle-Side) Congruence Postulate states that 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 is the ASA Congruence Postulate?

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The ASA (Angle-Side-Angle) Congruence Postulate states that 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 is the SSS Congruence Postulate?

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The SSS (Side-Side-Side) Congruence Postulate states that 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 does it mean for triangles to be congruent?

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Triangles are congruent when they have the same size and shape, which means all corresponding sides and angles are equal.

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What is a congruence statement?

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A congruence statement is a mathematical statement that indicates two geometric figures are congruent, typically written in the form of ΔABC ≅ ΔDEF.

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What is the significance of corresponding parts in congruence?

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In congruence, corresponding parts refer to the sides and angles of the triangles that match in size and measure, which are crucial for proving triangle congruence.

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What is the difference between congruence and similarity?

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Congruence means that two figures are identical in size and shape, while similarity means that two figures have the same shape but may differ in size.