Question

drag the similar figure into the table. angle measures are rounded to the nearest integer.
original figure
similar figure
4 37° 5
3

Explanation:

Step 1: Analyze the original figure (blue triangle)

The original figure is a right - angled triangle with angles \(37^{\circ}\), \(53^{\circ}\), \(90^{\circ}\) and side lengths 3, 4, 5. We can check the ratios of the sides: \(\frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\frac{1}{2}\), which means the sides are in proportion. Also, the angles of the purple triangle are \(37^{\circ}\), \(53^{\circ}\), \(90^{\circ}\) which are equal to the angles of the blue triangle. For similar triangles, the corresponding angles must be equal and the corresponding sides must be in proportion.

Step 2: Analyze the other triangles

• The green triangle has angles \(67^{\circ}\), \(23^{\circ}\), \(90^{\circ}\), which are different from the angles of the blue triangle, so it is not similar.
• The yellow triangle is an equilateral triangle with all angles \(60^{\circ}\), which is different from the angles of the blue right - angled triangle, so it is not similar.

Answer:

The purple right - angled triangle (with angles \(37^{\circ}\), \(53^{\circ}\), \(90^{\circ}\) and side lengths 6, 8, 10)