Are these rectangles similar? [br][br]Explain how you know.

Tyler wrote a proof that all rectangles are similar. Make the image Tyler describes in each step in his proof. [br][br]Which step makes a false assumption? [br][br]Why is it false?[br][br]1. Draw 2 rectangles. Label on [i]ABCD[/i] and the other [i]PQRS[/i].[br][br]2. Translate rectangle [i]ABCD[/i] by the directed line segment from [i]A[/i] to [i]P.[/i] [i]A'[/i] and [i]P[/i] now coincide.[br][br]3. Rotate rectangle [i]A'B'C'D' by angle [/i]D'A'S[i]. Segment A"D" [/i]now lies on ray [i]PS[/i].[br][br]4. Dilate rectangle [i]A"B"C"D"[/i] using center [i]A" [/i]and scale factor [math]\frac{PS}{AD}[/math].[br][br]5. Because all angles of a rectangle are right angles, segment [i]A'''B'''[/i] now lies on ray [i]PQ[/i]. [br](If [i]A'''B'''[/i] and [i]PQ[/i] don't coincide, reflect across [i]PS[/i].[br][br]6. Dilate rectangle [i]A'''B'''C'''D'''[/i] using center [i]A'''[/i] and scale factor [math]\frac{PQ}{AB}[/math].[br][br]7. Due to the symmetry of a rectangle, if 2 rectangles coincide on 2 sides, they must coincide on all sides[br][br]

Choose one statement from the list. Decide if it is true or not.[br][br]If it is true, write a proof.[br][br]If it is not true, provide a counterexample[br][br][list=1][*]All equilateral triangles are similar.[/*][*]All isosceles triangles are similar.[/*][*]All right triangles are similar.[/*][*]All circles are similar.[/*][/list]