Triangle Congruence Theorems

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What does the HL theorem stand for in triangle congruence?

Back

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 is the SSS theorem in triangle congruence?

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SSS 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 triangles are congruent.

Front

What does the SAS theorem state?

Back

SAS 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 triangles are congruent.

Front

What is the AAS theorem in triangle congruence?

Back

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.

Front

What does the ASA theorem state?

Back

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

Front

What is the significance of the HL theorem?

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The HL theorem is significant because it is a specific case of the SAS theorem that applies only to right triangles.

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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 the SSS theorem, you must show that all three sides of one triangle are equal to all three sides of another triangle.

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What is the difference between SAS and AAS theorems?

Back

SAS requires two sides and the included angle to be equal, while AAS requires two angles and a non-included side to be equal.

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Can the SSA condition prove triangle congruence?

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No, SSA (Side-Side-Angle) does not guarantee triangle congruence because it can lead to ambiguous cases.

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What is an example of using the ASA theorem?

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If triangle ABC has angles A and B equal to angles D and E in triangle DEF, and side AB is equal to side DE, then triangles ABC and DEF are congruent by ASA.