Triangle Congruence Proofs

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What is Triangle Congruence?

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Triangle congruence refers to the condition where two triangles are considered congruent if their corresponding sides and angles are equal.

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a criterion for triangle congruence 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 is the definition of CPCTC?

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CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, which is used to prove that corresponding angles and sides of congruent triangles are equal.

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What is the Reflexive Property?

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The Reflexive Property states that any geometric figure is congruent to itself, meaning that for any segment AB, AB ≅ AB.

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What is the Alternate Interior Angles Theorem?

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The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

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What is the Definition of Midpoint?

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The midpoint of a segment is the point that divides the segment into two equal parts.

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What does the term 'corresponding angles' mean?

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Corresponding angles are pairs of angles that are in the same position on two different parallel lines cut by a transversal.

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What is the Angle-Angle (AA) Criterion for triangle similarity?

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The AA Criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

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What is the significance of the Definition of Congruence?

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The Definition of Congruence states that two figures are congruent if they have the same shape and size.

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What is the purpose of a proof in geometry?

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A proof in geometry is a logical argument that establishes the truth of a statement or theorem based on previously established statements and axioms.