Triangle Similarity Theorem: Finding the Ratio between ABC and DEF

Question

According to which theorem are the triangles similar?

What is their ratio of similarity?

00:00 According to which theorem are the triangles similar? And what is the similarity ratio?

00:03 Let's find the similarity ratio between the sides

00:09 Let's substitute appropriate values according to the given data and find the ratio

00:12 This is the ratio, if it's equal for all sides then the triangles are similar

00:16 Let's check another pair of sides

00:25 The ratio matches

00:30 And let's check the last pair of sides

00:38 Here too the ratio matches

00:45 The triangles are similar according to SSS

00:49 And this is the solution to the question

Using the given data, the side ratios can be written as follows:

$\frac{FD}{AB}=\frac{X}{2X}=\frac{1}{2}$

$\frac{FE}{AC}=\frac{\frac{y}{2}}{y}=\frac{y}{2y}=\frac{1}{2}$

$\frac{DE}{BC}=\frac{2Z}{4Z}=\frac{2}{4}=\frac{1}{2}$

We can therefore deduce that the ratio is compatible with the S.S.S theorem (Side-Side-Side):

$\frac{FD}{AB}=\frac{FE}{AC}=\frac{DE}{BC}=\frac{1}{2}$

S.S.S., $\frac{1}{2}$