Question

1. a designer is trying different designs for a business logo. several of the logos are shown.

a. circle all of the logos that are similar to each other.
b. for the logos you identified, describe a sequence of transformations that takes one logo to the other.

Explanation:

A. Similar figures have proportional side lengths and congruent angles. The first, second, third, and fifth logos have the same shape (a square/rectangle attached to a right triangle) with proportional dimensions, while the fourth logo has a triangle that is not proportional to the others relative to its square.
B. To transform one similar logo to another, we use scaling (resizing) to match the side lengths, and can use translation (sliding) to reposition it if needed.

Answer:

A. The similar logos are:

1. Top logo (blue rectangle + red triangle)
2. Second logo (larger blue square + red triangle)
3. Third logo (small blue square + red triangle)
4. Bottom logo (blue rectangle + red triangle)

B. Example (transforming the third small logo to the second large logo):

1. Apply a dilation (scaling) with a scale factor greater than 1, centered at a chosen point, to increase the size of the small logo so its side lengths match the large logo.
2. Apply a translation (slide) to move the scaled logo to the position of the large logo.