Question

which of the following will be a pair of similar figures? select one answer: a a rectangle with width 3 and a rectangle with width 2.5 b a scalene triangle with a side length of 3 and a scalene triangle with a side length of 9 c a circle with radius 4 and a circle with radius 5 d a hexagon with a side length of 4 and a hexagon with a side length of 8

Explanation:

Step1: Recall Similar Figures Definition

Similar figures have proportional corresponding sides (or radii, diameters for circles) and equal corresponding angles. For circles, all circles are similar because their shape is defined by a single parameter (radius), and the ratio of radii determines the scale factor.

Step2: Analyze Option A

A rectangle with width 3 and a rectangle with width 2.9 – rectangles need all corresponding sides proportional. Just width info is insufficient; lengths could be arbitrary, so not necessarily similar.

Step3: Analyze Option B

A scalene triangle with a side length of 3 and a scalene triangle with a side length of 9. Scalene triangles have all sides of different lengths, but we only know one side each. Without info on other sides' proportions or angles, we can't confirm similarity.

Step4: Analyze Option C

A circle with radius 4 and a circle with radius 5. All circles are similar because the ratio of their radii (4:5) is constant, and circles have the same shape (defined by radius/diameter).

Step5: Analyze Option D

A hexagon with a side length of 4 and a hexagon with a side length of 8 – wait, no, the option says "a side length of 4 and a hexagon with a side length of 8"? Wait, original D: "A hexagon with a side length of 4 and a hexagon with a side length of 8"? Wait, no, the image shows D as "A hexagon with a side length of 4 and a hexagon with a side length of 8"? Wait, no, the user's image: D is "A hexagon with a side length of 4 and a hexagon with a side length of 8"? Wait, no, the text in D: "A hexagon with a side length of 4 and a hexagon with a side length of 8"? Wait, no, the original problem's D: "A hexagon with a side length of 4 and a hexagon with a side length of 8"? Wait, no, the user's image: D is "A hexagon with a side length of 4 and a hexagon with a side length of 8"? Wait, no, let's recheck. Wait, the key is: circles are always similar. So Option C is correct.

Answer:

C. A circle with radius 4 and a circle with radius 5