Triangle Similarity Investigation: Comparing Two Triangles with Sides 100, 80, and 62.5

Are the two triangles similar?

To find out if the triangles are similar, we can check if there is an appropriate similarity ratio between their sides.

The similarity ratio is the constant difference between the corresponding sides.

In this case, we can check if:

$\frac{62.5}{50}=\frac{100}{80}=\frac{100}{80}$

$\frac{62.5}{50}=\frac{125}{100}=1\frac{25}{100}=1\frac{1}{4}$

$\frac{100}{80}=\frac{10}{8}=1\frac{2}{4}=1\frac{1}{4}$

Therefore:$1\frac{1}{4}=1\frac{1}{4}=1\frac{1}{4}$

Therefore, we can say that there is a constant ratio of$1\frac{1}{4}$ between the sides of the triangles and therefore the triangles are similar.