Question

similarity - item 33750 select the two pairs of figures that are similar. angle measures are rounded to the nearest integer. images of triangles and rectangles with side lengths and angles

Explanation:

Step1: Check triangle similarity

For the two triangles:

• The first triangle has sides \(3\), \(4\), \(5\) and angles \(90^{\circ}\), \(53^{\circ}\), \(37^{\circ}\).
• The second triangle has sides \(6\), \(8\), \(10\). Since \(\frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\frac{1}{2}\), and all corresponding angles are equal (\(90^{\circ}\), \(53^{\circ}\), \(37^{\circ}\)), they are similar by SSS (Side - Side - Side) similarity criterion.

Step2: Check rectangle similarity

For the two rectangles (the green and brown ones):

• The green rectangle has sides \(2\) and \(4\).
• The brown rectangle has sides \(4\) and \(8\). Since \(\frac{2}{4}=\frac{4}{8}=\frac{1}{2}\), and all angles in rectangles are \(90^{\circ}\), they are similar (for rectangles, if the ratios of corresponding sides are equal, they are similar as all angles are equal).

Answer:

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