Decide mentally whether each statement is always true, sometimes true, or never true.

• If two figures are congruent, then they are similar.

• If two figures are similar, then they are congruent.

• If a triangle is dilated with the center of dilation at one of its vertices, the side lengths of the new triangle will change.

• If a triangle is dilated with the center of dilation at one of its vertices, the angle measures of the triangle will change.

1. Let’s look at a square and a rhombus.

   

   Priya says, “These polygons are similar because their side lengths are all the same.” Clare says, “These polygons are not similar because the angles are different.” Do you agree with either Priya or Clare? Explain your reasoning.
2. Now, let’s look at rectangles and .
   

   

   
   Jada says, “These rectangles are similar because all of the side lengths differ by 2.” Lin says, “These rectangles are similar. I can dilate and using a scale factor of 2 and and using a scale factor of 1.5 to make the rectangles congruent. Then I can use a translation to line up the rectangles.” Do you agree with either Jada or Lin? Explain your reasoning.

Your teacher will give you a card. Find someone else in the room who has a card with a polygon that is similar but not congruent to yours. When you have found your partner, work with them to explain how you know that the two polygons are similar.