Verify that the dilation is a similarity transformation

Using similar triangle

We notice that,

Both triangles have the same angle base

Then, <A ≈ <A

Also, from corresponding angle

<F ≈ <B

And < C ≈ <G

Using this, since the three angles of the triangles are equal, then we can write their similarities from their angle

∆F AG ≈ ∆BAC

Let assume one square of the graph represent one unit

So, ∆F AG ≈ ∆BAC

|F A| / ||BA| = |FG| / |BC| = |AG| / |AC|

|F A| = 9 Square units

|BA| = 3 Square units

|AC| = 2 Square units

|AG| = 6 Square units

|F A| / |BA| = |AG| / |AC|

|F A| / ||BA| = 9 / 3 = 3

|AG| / |AC| = 6 / 2 = 3

Then,

|F A| / |BA| = |AG| / |AC| = 3

Then,

The second option is correct

<A ≈ <A, |A F| / |AB| = |AG| / |AC| = 3