I hope that this isn't too late and that my explanation has helped rather than made things more confusing. Thus, if A X and AB/XY AC/XZ then ABC XYZ. This concept teaches students to decide whether or not two triangles are similar using SSS Similarity. You can then equate these ratios and solve for the unknown side, RT. SAS or Side-Angle-Side Similarity If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. 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. The SSS similarity theorem states that if the ratios comparing the corresponding sides of two triangles are all equal, then the two triangles are similar. 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: 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. SAS or Side-Angle-Side Similarity If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. 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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