Triangle Congruence Theorems

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What does the acronym SAS stand for in triangle congruence theorems?

Back

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

Front

What does the acronym AAS stand for in triangle congruence theorems?

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AAS stands for Angle-Angle-Side, which states 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, then the triangles are congruent.

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What does the acronym HL stand for in triangle congruence theorems?

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HL stands for Hypotenuse-Leg, which applies specifically to right triangles. It states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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What is the definition of triangle congruence?

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Triangle congruence means that two triangles are identical in shape and size, meaning all corresponding sides and angles are equal.

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What is the SSS triangle congruence theorem?

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

Front

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

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

Front

What is the importance of the included angle in the SAS theorem?

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The included angle is crucial in the SAS theorem because it is the angle formed between the two sides being compared, ensuring that the triangles are congruent based on their specific configuration.

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Can two triangles be congruent if only two sides are equal?

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No, two triangles cannot be proven congruent with only two sides equal unless the included angle is also known (SAS) or additional information is provided.

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What is the difference between congruence and similarity in triangles?

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

Front

What is the criteria for triangle congruence using the AAS theorem?

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The AAS theorem requires 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.