POSSIBLE POINTS: 1 This is an invalid proof that all isosceles triangles are similar. 1. Draw 2 isosceles triangles ABC and DEF where AC-BC and DF-EF. 2. Dilate triangle ABC to a new triangle A'B'C using center C and scale factor So that A'C-B'C=DF=EF. 3. Translate by directed line segment CF to take A'B'C to a new triangle A"B"F. Since translation preserves distance, A"F=A'C=DF and B"F=B'C=EF 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B"F=EF, we can rotate using center F to take B" to E 6. We have now established a sequence of dilations, translations, and rotations that takes A to D. B to E, and C to F, so the triangles are similar. Which step is invalid and why? O Step 2 is invalid. Using scale factor - would not result in A'C-B'C-DF-EF Step 5 is invalid. Step 4 was a rotation using the same center and took A" to D so it already also took B" to E. Another rotation in Step 5 would O not then take B" to E. O Step 6 is invalid. Transformations act on the whole plane, so when we rotate in Step 5 to take B" to E, our sequence no longer takes A to D. Step 6 is invalid. There is not a step that includes a rotation using center F that takes C" to F. therefore our sequence does not take C to F