Triangle Congruence Theorems

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What does the HL theorem stand for in triangle congruence?

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

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What does the AAS theorem stand for in triangle congruence?

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AAS stands for Angle-Angle-Side theorem, 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 SSS theorem stand for in triangle congruence?

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

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What does the ASA theorem stand for in triangle congruence?

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ASA 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 corresponding included side of another triangle, then the triangles are congruent.

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What is the SSA condition in triangle congruence?

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SSA stands for Side-Side-Angle, which is not a valid theorem for proving triangle congruence because it can lead to ambiguous cases.

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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, which means their corresponding sides and angles are equal, allowing for various applications in proofs and real-world problems.

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

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To prove triangles are congruent using AAS, show that two angles and a non-included side of one triangle are equal to the corresponding two angles and non-included side of another triangle.

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

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To prove triangles are congruent using ASA, demonstrate that two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

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

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To prove triangles are congruent using SSS, establish that all three sides of one triangle are equal to all three sides of another 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, meaning if two triangles are congruent, their angles match in measure.