Triangle Congruency Theorems

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What does the acronym ASA stand for in triangle congruency?

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Angle-Side-Angle: A triangle is congruent if two angles and the included side are equal to two angles and the included side of another triangle.

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What does the acronym AAS stand for in triangle congruency?

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Angle-Angle-Side: A triangle is congruent if two angles and a non-included side are equal to two angles and a corresponding non-included side of another triangle.

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What does the acronym SAS stand for in triangle congruency?

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Side-Angle-Side: A triangle is congruent if two sides and the included angle are equal to two sides and the included angle of another triangle.

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What does the acronym SSS stand for in triangle congruency?

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Side-Side-Side: A triangle is congruent if all three sides are equal to the corresponding sides of another triangle.

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What does the acronym HL stand for in triangle congruency?

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Hypotenuse-Leg: A theorem used for right triangles stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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When can the AAS theorem be applied?

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The AAS theorem can be applied when two angles and a non-included side of one triangle are known to be equal to two angles and the corresponding non-included side of another triangle.

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When can the ASA theorem be applied?

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The ASA theorem can be applied when two angles and the included side of one triangle are known to be equal to two angles and the included side of another triangle.

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When can the SAS theorem be applied?

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The SAS theorem can be applied when two sides and the included angle of one triangle are known to be equal to two sides and the included angle of another triangle.

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When can the SSS theorem be applied?

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The SSS theorem can be applied when all three sides of one triangle are known to be equal to the three sides of another triangle.

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When can the HL theorem be applied?

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The HL theorem can be applied specifically to right triangles when the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle.