Triangle Congruence Theorems

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What does SAS stand for in triangle congruence theorems?

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SAS stands for Side-Angle-Side, which is a theorem that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

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What does ASA stand for in triangle congruence theorems?

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ASA stands for Angle-Side-Angle, which is a theorem that states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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What does AAS stand for in triangle congruence theorems?

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AAS stands for Angle-Angle-Side, which is a theorem that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

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What does the SSS theorem state?

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The SSS theorem stands for Side-Side-Side, which states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

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What is the AAA condition in triangle congruence?

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AAA stands for Angle-Angle-Angle, which states that if three angles of one triangle are congruent to three angles of another triangle, the triangles are similar but not necessarily congruent.

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What is the Reflexive Property in geometry?

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The Reflexive Property states that any geometric figure is congruent to itself, meaning \overline{AB} \cong \overline{AB}.

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What is the Vertical Angles Theorem?

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The Vertical Angles Theorem states that when two lines intersect, the opposite (vertical) angles are congruent.

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What is the purpose of triangle congruence theorems?

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Triangle congruence theorems are used to prove that two triangles are congruent, meaning they have the same size and shape.

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How can you prove triangles are congruent using the SAS theorem?

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To prove triangles are congruent using the SAS theorem, you need to show that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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What is the significance of congruent triangles in geometry?

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Congruent triangles are significant because they allow us to infer properties about the triangles, such as side lengths and angle measures, which can be used in various geometric proofs and applications.