Geometry Help Triangles Proving Congruence with SSS and SAS. I hope that this isn't too late and that my explanation has helped rather than made things more confusing. Triangle Congruence - SSS and SAS We have learned that triangles are congruent if their. You can then equate these ratios and solve for the unknown side, RT. If, there are no possible triangles (right figure). If, there is one possible triangle (middle figure). If, there are two possible triangles satisfying the given conditions (left figure). If you want to know how this relates to the disjointed explanation above, 30/12 is like the ratio of the two known side lengths, and the other ratio would be RT/8. Specifying two adjacent side lengths and of a triangle (with ) and one acute angle opposite does not, in general, uniquely determine a triangle. Now that we know the scale factor we can multiply 8 by it and get the length of RT: If you solve it algebraically (30/12) you get: I like to figure out the equation by saying it in my head then writing it out: side-angle-side theorem, also called SAS theorem, in Euclidean geometry, theorem stating that if two corresponding sides in two triangles are of the same length, and the angles between these sides (the included angles) in those two triangles are also equal in measure, then the two triangles are congruent (having the same shape and size). In this case you have to find the scale factor from 12 to 30 (what you have to multiply 12 by to get to 30), so that you can multiply 8 by the same number to get to the length of RT. Keyterms: Geometry, Triangle, Congruence in the triangles, Angle, Area of Triangle, SSS, SAS, ASA, AAS, RHS. The first step is always to find the scale factor: the number you multiply the length of one side by to get the length of the corresponding side in the other triangle (assuming of course that the triangles are congruent).
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