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| Summary |
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| SAS Axiom: If two triangles have two sides of one equal to two sides of the other, each to each, and angles included by these sides are equal, then the triangles are congruent. |
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| AAS Axiom: If two triangles have two angles of one equal to two angles of the other, each to each and also one side of one equal to the corresponding side of the other, then the triangles are congruent. |
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| SSS Axiom: If two triangles have three sides of one equal to three sides of the other each to each, then the triangles are congruent. |
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| RHS Axiom: If two right triangles have their hypotenuses equal and one side of one equal to one side of the other, then the triangles are congruent. |
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