Triangle Congruence Theorems

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

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SAS stands for Side-Angle-Side, which states that 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.

Front

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

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ASA stands for Angle-Side-Angle, which states that 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.

Front

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

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

Front

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

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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 congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

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What is the significance of the Hypotenuse-Leg (HL) theorem in triangle congruence?

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The HL theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

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How can you determine if two triangles are congruent using the SSS theorem?

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To determine if two triangles are congruent using the SSS theorem, measure all three sides of both triangles. If all three sides of one triangle are equal to the corresponding sides of the other triangle, then the triangles are congruent.

Front

What is the difference between congruent triangles and similar triangles?

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Congruent triangles have the same size and shape, meaning all corresponding sides and angles are equal. Similar triangles have the same shape but not necessarily the same size; their corresponding angles are equal, and their sides are proportional.

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What is the Angle-Side relationship in triangle congruence?

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The Angle-Side relationship states that the side opposite the larger angle in a triangle is longer than the side opposite the smaller angle.

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Can two triangles be congruent if only one side is known to be equal?

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No, two triangles cannot be proven congruent with only one side known to be equal. At least two sides and the included angle or two angles and the included side must be known.

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What is the purpose of using triangle congruence theorems in geometry?

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Triangle congruence theorems are used to prove that two triangles are congruent, which helps in solving problems related to angles, sides, and other geometric properties.