Which pairs of polygons are similar?

In order to determine which pairs of figures are indeed similar, you must compare the ratios of one side to another.

 

A) \(\frac{18}{27}=\frac{10}{15}\)

 

Simplifying both the fractions into simplest terms, \(\frac{2}{3}=\frac{2}{3}\), which indeed proves both figures to be similar.

 

B) Do the same thing with the rectangles.

 

\(\frac{7}{10}=\frac{14}{18}\)

 

Doing the exact process, \(\frac{7}{10}\neq\frac{7}{9}\), so these figures here are not congruent.

 

C) All equilateral triangles are similar.

 

D) Yet again, check the similarity by comparing the ratio.

 

\(\frac{18}{24}=\frac{24}{32}\)

 

Simplifying in simplest terms, \(\frac{3}{4}=\frac{3}{4}\), so this pair of figures are similar. 

 

A, C, and D are all pairs of figures that are similar.