Triangle Congruence Theorems

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What does SSS stand for in Triangle Congruence Theorems?

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

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What does ASA stand for in Triangle Congruence Theorems?

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ASA stands for Angle-Side-Angle, 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.

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What does AAS stand for in Triangle Congruence Theorems?

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AAS stands for Angle-Angle-Side, 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 SAS stand for in Triangle Congruence Theorems?

Back

SAS stands for Side-Angle-Side, 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.

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What does HL stand for in Triangle Congruence Theorems?

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HL stands for Hypotenuse-Leg, which applies to right triangles and states 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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How can you prove triangles are congruent using SSS?

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To prove triangles are congruent using SSS, show that all three sides of one triangle are equal to the three sides of another triangle.

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How can you prove triangles are congruent using ASA?

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

Front

How can you prove triangles are congruent using AAS?

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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 two angles and the corresponding non-included side of another triangle.

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How can you prove triangles are congruent using SAS?

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To prove triangles are congruent using SAS, show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

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How can you prove triangles are congruent using HL?

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To prove triangles are congruent using HL, show that the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle.