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Carol Fisher's Homepage Geometry Table of Contents |
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THEOREM: ASA CONGRUENCE A unique triangle is formed by two angles and the included side. Therefore, 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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THEOREM: AAS CONGRUENCE A unique triangle is formed by two angles and a non-included side. Therefore, if two angles and the side opposite one of them in a triangle are equal to the corresponding parts in another triangle, then the triangles are congruent. |
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THEOREM: SAS CONGRUENCE A unique triangle is formed by two sides and an included angle. Therefore, 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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THEOREM: SSS CONGRUENCE A unique triangle is formed by specifying three sides of a triangle, where the the longest side (if there is one) is less than the sum of the two shorter sides. Therefore, if three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent. |
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THEOREM: THE TRIANGLE INEQUALITY THEOREM The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Conversely, if three numbers satisfy the property that the sum of any two of them exceeds the third, then there exists a triangle with these lengths for its sides. |
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Geometry Table of Contents © 2004 Carol J.V. Fisher |
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