Final answer:
The correct statement for Mr. Ortiz's design using similar triangles is that the triangles have corresponding angles that are congruent, meaning they have the same shape but not necessarily the same size.
Step-by-step explanation:
When Mr. Ortiz used similar triangles to make a design, it implies that all triangles within that design must have certain proportions and angles the same. The correct statement about the triangles in the design must be C. They have corresponding angles that are congruent. Similar triangles are defined by having the same shape, but not necessarily the same size. They maintain the same angles, and their sides are in proportion to each other. However, they do not need to have corresponding sides that are congruent, which would imply they are identical in size, nor do they have to be the exact same size in general. Therefore, the triangles could differ in size but still be similar; hence, they would have the same shape, i.e., angle measurements, but different side lengths that are proportional.
For example, if we have a triangle with angles measuring 30°, 60°, and 90°, and we create a similar triangle by doubling all the angles, the new triangle will have angles measuring 60°, 120°, and 180°, which is still a triangle with the same shape, but not the same size.
In Mr. Ortiz's design, the triangles are similar, but they may not necessarily be the same size and shape. However, their corresponding angles will have the same measure.