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 SSS stand for in triangle congruence?

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SSS stands for 'Side-Side-Side', a theorem stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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What does SAS stand for in triangle congruence?

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SAS stands for 'Side-Angle-Side', a theorem stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

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What does AAS stand for in triangle congruence?

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

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What does ASA stand for in triangle congruence?

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ASA stands for 'Angle-Side-Angle', a theorem stating that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, the triangles are congruent.

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What is the significance of the corresponding parts of congruent triangles?

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The corresponding parts of congruent triangles are equal, which means that if two triangles are proven to be congruent, all their corresponding sides and angles are also equal.

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What is the difference between SSA and other congruence theorems?

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SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

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How can you prove that two triangles are congruent using the SSS theorem?

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To prove triangles are congruent using SSS, show that all three sides of one triangle are equal to the three sides of another triangle.

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What is the relationship between angles in congruent triangles?

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In congruent triangles, corresponding angles are equal, meaning if two triangles are congruent, their angles match in measure.