Triangle Congruence Theorems

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What does the HL theorem stand for in triangle congruence?

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The HL theorem stands for Hypotenuse-Leg theorem, which 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 two triangles are congruent.

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What does the SSS theorem state in triangle congruence?

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

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What is the ASA theorem in triangle congruence?

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The ASA theorem stands for Angle-Side-Angle theorem, 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 two triangles are congruent.

Front

What does the SAS theorem state in triangle congruence?

Back

The SAS theorem stands for Side-Angle-Side theorem, 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 two triangles are congruent.

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What is the significance of congruent triangles in geometry?

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Congruent triangles have the same size and shape, meaning all corresponding sides and angles are equal, which is essential for solving various geometric problems.

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

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To prove two triangles are congruent using the SSS theorem, you must show that all three sides of one triangle are equal to the three sides of the other triangle.

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What is the relationship between the angles in congruent triangles?

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In congruent triangles, corresponding angles are equal, which means if two triangles are congruent, their angles will also be congruent.

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Can the HL theorem be used for non-right triangles?

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No, the HL theorem can only be used for right triangles, as it specifically involves the hypotenuse.

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What is the difference between ASA and AAS in triangle congruence?

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ASA (Angle-Side-Angle) requires the included side between two angles to be equal, while AAS (Angle-Angle-Side) requires two angles and a non-included side to be equal.

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What is the criteria for using the SAS theorem?

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The criteria for using the SAS theorem is that two sides and the included angle of one triangle must be equal to two sides and the included angle of another triangle.