Triangle Congruence Review for Test

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What does the acronym SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states 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.

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What does the acronym AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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 acronym ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states 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 does the acronym SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states 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 is the HL theorem in triangle congruence?

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

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Can two triangles be congruent if only two angles are known?

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No, knowing only two angles does not guarantee congruence; the third angle can vary, leading to different triangle sizes.

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What is the significance of the included angle in the SAS theorem?

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence in the SAS theorem.

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

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

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What is the difference between ASA and AAS?

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ASA requires the included side between two angles to be equal, while AAS allows for a non-included side to be equal.

Front

What is a necessary condition for using the SSS theorem?

Back

All three sides of one triangle must be equal to all three sides of another triangle.