Tyler was trying to prove that all rhombuses are similar. He thought, "I draw 2 rhombuses, I can find citations that will take one thombus exactly onto the other." Then he wrote a proof. All rhombuses are not similar. Which steps in Tyler's proof have flaws? Explain what is wrong with each step that is wrong.
Step 1: Let ABCD and WXYZ be rhombuses. By the definition of a rhombus, AB BC CDADA and WX EXYYZEZW.
Step 2: Dilate rhombus ABCD by the scale factor given by WX Side A'B'will be the same length as wx because of how I chose the scale factor, Because all sides of a rhombus are congruent.
BC will be the same length as WX and therefore the same length as XY, CD' will be the same length as YZ, and A'D' will be the same length as W2. That means all the corresponding sides of
A'B'C'D' and WXYZ will be the same length
Step 3: It all the sides in 2 figures are proportional, then those 2 figures are similar, so there must be a sequence of transformations that take ABCD onto WXYZ using dilations and rigid motions.
Step 4: Translate A'B'C'D' by the directed line segment AW so that A" and W coincide.
Step 5. Rotate A'B'C"D" by angle B"WX so that " and X coincide. Now segments A"B" and WX coincide.
Step 6: If needed, reflect A"8°C D over segment WX so that D" and Z are on the same side of WX. Now segments AD" and WZ coincide.
Step 7: Once 3 vertices of the rhombus are lined up, the other vertex has to line up as well or else the shapes wouldn't be rhombuſes. So, we have shown we can use rigid motions and dilations
to line up any 2 rhombuses, and therefore, all rhombuses are similar