Triangle Congruence Theorems

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What does ASA stand for in triangle congruence theorems?

Back

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

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What does HL stand for in triangle congruence theorems?

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

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What does SSS stand for in triangle congruence theorems?

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

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What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (or vertical) angles are congruent.

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What is the purpose of triangle congruence theorems?

Back

The purpose of triangle congruence theorems is to determine whether two triangles are congruent, meaning they have the same size and shape.

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What is the difference between ASA and AAS?

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

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Can the SSS theorem be used for right triangles?

Back

Yes, the SSS theorem can be used for all types of triangles, including right triangles.

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What is the significance of the included side in the ASA theorem?

Back

The included side in the ASA theorem is the side that is between the two angles being considered; it must be congruent for the triangles to be proven congruent.

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What is a common misconception about the HL theorem?

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A common misconception is that the HL theorem can be used for all triangles; however, it only applies to right triangles.

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

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