This is an incorrect proof that all isosceles triangles are similar. Explain why the proof is incorrect.

Step 1. Draw 2 isosceles triangles and where and .

Step 2. Dilate triangle to a new triangle using center and a scale factor of , so that .

Step 3. Translate by directed line segment to take to a new triangle . Because translation preserves distance,  and .

Step 4. Because  , we can rotate using center to take to .

Step 5. Because  , we can rotate using center to take to .

Step 6. We have now established a sequence of dilations, translations, and rotations that takes  to , to , and to , so the triangles are similar.