Question

select the two pairs of figures that are similar. angle measures are rounded to the nearest integer.

Explanation:

Step1: Check similarity for triangles

For two triangles to be similar, their corresponding angles must be equal and their sides must be in proportion.
The first triangle has sides \(3,4,5\) and angles \(37^{\circ},53^{\circ},90^{\circ}\).
The second triangle has sides \(6,8,10\).
We can check the ratio of sides: \(\frac{3}{6}=\frac{1}{2},\frac{4}{8}=\frac{1}{2},\frac{5}{10}=\frac{1}{2}\).
Since the ratios of corresponding sides are equal and angles are equal (\(37^{\circ},53^{\circ},90^{\circ}\) in both), these two triangles are similar.

Step2: Check similarity for rectangles

For two rectangles to be similar, the ratio of their length and width must be equal.
The green rectangle has length \(4\) and width \(2\), ratio \(\frac{4}{2} = 2\).
The brown rectangle has length \(8\) and width \(4\), ratio \(\frac{8}{4}=2\).
Since the ratios of length to width are equal (\(2\) for both), these two rectangles are similar.
The blue rectangle (length \(10\), width \(4\), ratio \(\frac{10}{4}=\frac{5}{2}\)) and the pink square (length \(4\), width \(4\), ratio \(1\)) are not similar to any other in their group as their ratios don't match.

Answer:

The two pairs of similar figures are the pair of triangles and the pair of rectangles (the green and brown rectangles).