Find the Similarity Ratio: Comparing Triangles ΔGHF, ΔNOM and ΔABC in a Nested Structure

Question

What is the similarity ratio between triangles ΔGHF and ΔABC?

00:00 Find the similarity ratio between the triangles

00:03 The equilateral triangles

00:08 In an equilateral triangle all angles are equal to 60

00:16 The triangles are similar because all angles are equal

00:33 This is the similarity ratio between the triangles

00:52 Equal sides

01:01 Let's substitute appropriate side values according to the given data

01:06 And this is the solution to the question

To solve this problem, we need to calculate the similarity ratio between $\Delta GH F$ and $\Delta ABC$ . Since both triangles are equilateral:

The side length of $\Delta ABC$ is $18$ , and the side length of $\Delta GH F$ is $2$ .
The similarity ratio $\frac{\text{side of } \Delta ABC}{\text{side of } \Delta GHF}$ is:

\frac{18}{2} = 9.

Therefore, the similarity ratio between triangles $\Delta GHF$ and $\Delta ABC$ is $9$ . The correct choice is:

$\frac{AB}{GF}=\frac{AC}{FH}=9$ .

$\frac{AB}{GF}=\frac{AC}{FH}=9$