Congruent Triangles & Proofs

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a postulate 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 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 postulate 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 triangles are congruent.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a postulate that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are 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. For example, triangle ABC is congruent to triangle ABC.

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What is the purpose of triangle congruence postulates?

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Triangle congruence postulates are used to determine if two triangles are congruent based on specific criteria involving their sides and angles.

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How can you prove triangles are congruent using the SSS postulate?

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To prove triangles are congruent using the SSS postulate, you must show that all three corresponding sides of the triangles are equal in length.

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

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To prove triangles are congruent using the SAS postulate, you must show that 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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How can you prove triangles are congruent using the AAS postulate?

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To prove triangles are congruent using the AAS postulate, you must show that two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side 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 have the same size and shape, which allows for the application of various geometric principles and theorems.

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What is the difference between congruence and similarity in triangles?

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