Question

show that the triangles are similar by measuring the lengths of their sides and comparing the ratios of their corresponding sides

Answer 1

Step-by-step explanation

The ratio between corresponding sides of similar triangles is constant - in other words, the ratio between each pair of corresponding sides gives the same value.

As shown in the questions, the ratios between corresponding sides are,

`\begin{gathered} (DE)/(AB)=(3)/(2)=1.5 \\ (DF)/(AC)=(1.5)/(1)=1.5 \\ (EF)/(BC)=(2.4)/(1.6)=1.5 \end{gathered}`

Since the three ratios between corresponding sides are the same, 1.5, the triangles are similar.