Answer:
7) Similar; 8) not similar; 9) ⅔; 10) ⅘
Step-by-step explanation:
Two polygons are similar if
- their corresponding angles are congruent and
- the ratios of their corresponding sides are equal
7) Trapezoids
Corresponding angles are congruent.
[tex]\dfrac{30}{12} = \dfrac{15.5}{6.2} = \dfrac{40 }{16}} = \dfrac{5}{2}[/tex]
Corresponding sides are in the same ratio, so the trapezoids are similar.
8) Rectangles
Corresponding angles are congruent.
[tex]\text{Ratio of bases} =\dfrac{42}{35} = \dfrac{7}{5}\\\\\text{Ratio of sides} =\dfrac{24}{25}[/tex]
The ratios are different, so the rectangles are not similar.
In similar polygons, the ratio of the lengths of their corresponding sides (the scale factor) is the same.
9. Quadrilaterals
[tex]\text{Scale factor} = \dfrac{10}{15} = \mathbf{\dfrac{2}{3}}[/tex]
10. Trapezoids
[tex]\text{Scale factor} = \dfrac{16}{20} = \mathbf{\dfrac{4}{5}}[/tex]
