[img]data:image/png;base64,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[/img][br][br]Are these rectangles similar? Explain how you know.

[size=150]Tyler wrote a proof that all rectangles are similar. Make the image Tyler describes in each step in his proof. Which step makes a false assumption? Why is it false?[/size][br][br][list][*]Draw 2 rectangles. Label one [math]ABCD[/math] and the other [math]PQRS[/math].[/*][*]Translate rectangle [math]ABCD[/math] by the directed line segment from [math]A[/math] to [math]P[/math]. [math]A'[/math] and [math]P[/math] now coincide. The points coincide because that’s how we defined our translation.[/*][*]Rotate rectangle [math]A'B'C'D'[/math] by angle [math]D'A'S[/math]. Segment [math]A''D''[/math] now lies on ray [math]PS[/math]. The rays coincide because that’s how we defined our rotation.[/*][*]Dilate rectangle [math]A''B''C''D''[/math] using center [math]A''[/math] and scale factor [math]\frac{PS}{AD}[/math]. Segments [math]A'''D'''[/math] and [math]PS[/math] now coincide. The segments coincide because A'' was the center of the rotation, so [math]A''[/math] and [math]P[/math] don’t move, and since [math]D''[/math] and [math]S[/math] are on the same ray from [math]A''[/math], when we dilate [math]D''[/math] by the right scale factor, it will stay on ray [math]PS[/math] but be the same distance from [math]A''[/math] as [math]S[/math] is, so [math]S[/math] and [math]D'''[/math] will coincide.[/*][*]Because all angles of a rectangle are right angles, segment [math]A'''B'''[/math] now lies on ray [math]PQ[/math]. This is because the rays are on the same side of [math]PS[/math] and make the same angle with it. (If [math]A'''B'''[/math] and [math]PQ[/math] don’t coincide, reflect across [math]PS[/math] so that the rays are on the same side of [math]PS[/math].)[/*][*]Dilate rectangle [math]A'''B'''C'''D'''[/math] using center [math]A'''[/math] and scale factor [math]\frac{PQ}{AB}[/math]. Segments [math]A''''B''''[/math] and [math]PQ[/math] now coincide by the same reasoning as in step 4.[/*][*]Due to the symmetry of a rectangle, if 2 rectangles coincide on 2 sides, they must coincide on all sides.[/*][/list][*][/*]

[size=150]Statements:[br][list=1][*][size=150]All equilateral triangles are similar.[/size][/*][*][size=150]All isosceles triangles are similar.[/size][/*][*][size=150]All right triangles are similar.[/size][/*][*][size=150]All circles are similar.[/size][/*][/list][/size][br]If it is true, write a proof. If it is not, provide a counterexample.

Repeat with another statement.[br]

They are similar. What are the possible dimensions of these golden rectangles? Explain or show your reasoning.