Question

part two: determine if each pair of figures is similar and state why or why not. show all of your work. 3. 16 10 15.4 15.4 8.4 8.4 13 24 4. 18 63 14 65° 14 49 49 18 65° 63

Explanation:

Step1: Recall similarity condition for polygons

Two polygons are similar if their corresponding angles are equal and corresponding sides are in proportion.

Step2: Check side - length ratios for the first pair of trapezoids

For the trapezoids, find the ratios of corresponding sides.
The ratio of the top - sides is $\frac{16}{10}=\frac{8}{5}=1.6$.
The ratio of the bottom - sides is $\frac{13}{24}\approx0.54$.
Since $\frac{8}{5}
eq\frac{13}{24}$, the sides are not in proportion. So the first pair of trapezoids is not similar.

Step3: Check side - length ratios for the second pair of parallelograms

For the parallelograms, the ratio of the short sides is $\frac{14}{49}=\frac{2}{7}\approx0.29$.
The ratio of the long sides is $\frac{18}{63}=\frac{2}{7}\approx0.29$.
The corresponding angles of parallelograms are equal (opposite angles of a parallelogram are equal and for two parallelograms with one pair of corresponding angles equal, all corresponding angles are equal). Since the corresponding sides are in proportion ($\frac{14}{49}=\frac{18}{63}$) and corresponding angles are equal, the second pair of parallelograms is similar.

Answer:

1. The pair of trapezoids is not similar because the ratios of their corresponding sides are not equal.
2. The pair of parallelograms is similar because their corresponding angles are equal and corresponding sides are in proportion.