Triangle Congruency

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What is Triangle Congruency?

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Triangle congruency 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 SAS stand for in triangle congruency?

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

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What does ASA stand for in triangle congruency?

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ASA stands for Angle-Side-Angle, a criterion for triangle congruency 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 AAA stand for in triangle congruency?

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AAA stands for Angle-Angle-Angle, which indicates that if two triangles have equal corresponding angles, they are similar but not necessarily congruent.

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What does SSA stand for in triangle congruency?

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SSA stands for Side-Side-Angle, which is not a valid criterion for triangle congruency as it can lead to ambiguous cases.

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If ΔABC ≅ ΔDEF, what can be inferred about their corresponding sides and angles?

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If ΔABC ≅ ΔDEF, then the corresponding sides AB = DE, BC = EF, AC = DF and the corresponding angles ∠A = ∠D, ∠B = ∠E, ∠C = ∠F.

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What is the significance of the congruence statement ΔFGH ≅ ΔVWH?

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The congruence statement ΔFGH ≅ ΔVWH indicates that triangles FGH and VWH are congruent, meaning all corresponding sides and angles are equal.

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

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

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What is the difference between congruence and similarity in triangles?

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

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What is the purpose of using congruence statements in geometry?

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Congruence statements are used to clearly express the relationship between two congruent figures, indicating which parts correspond to each other.