Triangle Congruency

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What is Triangle Congruency?

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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 the Side-Angle-Side (SAS) Congruence Postulate state?

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The SAS Congruence Postulate states that if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is also equal, then the two triangles are congruent.

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What does the Angle-Side-Angle (ASA) Congruence Postulate state?

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The ASA Congruence Postulate states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.

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What does the Side-Side-Side (SSS) Congruence Postulate state?

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The SSS Congruence Postulate states that if all three sides of one triangle are equal to all three sides of another triangle, then the two triangles are congruent.

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What is the Hypotenuse-Leg (HL) Theorem?

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The HL 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 Angle-Angle-Angle (AAA) condition?

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The AAA condition states that if two triangles have equal corresponding angles, they are similar, but not necessarily congruent.

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What information is needed to prove triangles are congruent using SAS?

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To prove triangles are congruent using SAS, you need two sides and the included angle of one triangle to be equal to the corresponding two sides and included angle of the other triangle.

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

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To prove triangles are congruent using ASA, you need two angles and the included side of one triangle to be equal to the corresponding two angles and included side of the other triangle.

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What information is needed to prove triangles are congruent using SSS?

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To prove triangles are congruent using SSS, you need all three sides of one triangle to be equal to all three sides of the other triangle.

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What is the significance of congruency in triangles?

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Congruency in triangles is significant because it allows us to conclude that two triangles are identical in shape and size, which is useful in various applications in geometry and real-world problems.