Question

1. are the two figures similar? if not, why not?

a. yes, similar.
b. no, corresponding angles are not congruent.
c. no, corresponding sides are not proportional.
d. no, different shapes.

1. the two figures are similar. find the length of the missing side and solve for x.

a. side = 13
b. side = 12
c. side = 11
d. side = 10

1. select all that apply. two polygons are similar if ______.

a. corresponding angles are similar.
b. corresponding side lengths are proportional.
c. corresponding angles are congruent.
d. corresponding sides are parallel.

Explanation:

Step1: Check similarity conditions

For two polygons to be similar, corresponding angles must be congruent and corresponding sides must be proportional.

Step2: Analyze problem 2

In problem 2, the corresponding angles are not congruent (e.g., \(130^{\circ}\) vs \(120^{\circ}\)). So they are not similar.

Step3: Solve problem 4

For similar triangles, \(\frac{12}{8}=\frac{15}{x}\). Cross - multiply: \(12x = 8\times15\), \(12x=120\), \(x = 10\).

Step4: Analyze problem 6

By the definition of similar polygons, corresponding angles are congruent (not just similar, congruent means equal measure) and corresponding side lengths are proportional.

Answer:

1. B. No, corresponding angles are not congruent.
2. D. side = 10
3. B. Corresponding side lengths are proportional; C. Corresponding angles are congruent.