Question

1. determine similar
2. similar
3. similar
4. similar

Explanation:

Step1: Recall similarity criteria

For two polygons to be similar, their corresponding angles must be equal and corresponding - side lengths must be in proportion.

Step2: Analyze the first pair of triangles

For the first pair of right - angled triangles:
The ratios of corresponding sides are $\frac{6}{3.2}=\frac{15}{8}$ and $\frac{10}{5.33}\approx\frac{15}{8}$ (since $5.33=\frac{16}{3}$). Also, the right - angles are equal. So, they are similar.

Step3: Analyze the second pair of trapezoids

For the trapezoids, the ratios of corresponding sides: $\frac{15.4}{8.4}=\frac{11}{6}$, $\frac{13}{8}=\frac{13}{8}$, $\frac{16}{10}=\frac{8}{5}$. Since the ratios of corresponding sides are not equal, they are not similar.

Step4: Analyze the third pair of rectangles

For the rectangles, the ratio of the longer sides is $\frac{72}{12} = 6$ and the ratio of the shorter sides is $\frac{48}{10}=4.8$. Since the ratios of corresponding sides are not equal, they are not similar.

Step5: Analyze the fourth pair of parallelograms

For the parallelograms, the corresponding angles are equal ($65^{\circ}$). The ratio of corresponding sides: $\frac{18}{63}=\frac{2}{7}$, $\frac{14}{49}=\frac{2}{7}$. So, they are similar.

Answer:

The first and fourth pairs of polygons are similar, while the second and third pairs are not.