Question

Bryan purchases two triangular wall shelves. The sides of each shelf are 8 inches, 10 inches, and 12 inches. He's trying to build a similar, larger triangular shelf to place between the two smaller shelves. Which of the dimensions can Bryan use for the larger shelf so that it is similar to the ones he purchased? Justify why the three triangles are similar.
A) 4 inches, 5 inches, and 6 inches; All of the side lengths of the smaller triangles have been multiplied by 1/2, which guarantees side-side-side similarity.

B) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-side-side similarity.

C) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-angle-side similarity.

D) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees angle-angle-side similarity.
Eliminate

Answer 1

The correct answer is letter B) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-side-side similarity. Similar angles shows congruence when their sides are proportional.