Coordinate plane with triangles efg and ghi with e at negative 6 comma 2, f at negative 2 comma 6, g at negative 2 comma 2, h at negative 2 comma 4, and i at 0 comma 2
which set of transformations would prove δefg ~ δghi?
translate δghi by the rule (x − 2, y + 0), and reflect δg′h′i′ over x = −4.
reflect δghi over x = −2, and translate δg′h′i′ by the rule (x − 2, y + 0).
translate δghi by the rule (x + 0, y + 2), and dilate δg′h′i′ by a scale factor of 2 from point h.
reflect δghi over x = −2, and dilate δg′h′i′ by a scale factor of 2 from point g.

The set of transformation would prove ΔEFG ~ ΔGHI is "Reflect ΔGHI

over x = −2, and dilate ΔG′H′I′ by a scale factor of 2 from point G" ⇒

last answer

Step-by-step explanation:

* Lets revise the reflection and dilation

- A reflection is a transformation where each point in a shape appears

 at an equal distance on the opposite side of the line of reflection

- Reflection doesn't change the size of the original figure

- A dilation is a transformation that produces an image that is the same

 shape as the original, but is a different size

- The dilation has a scale factor and center of dilation

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

* Lets solve the problem

- The vertices of Δ EFG are:

# E = (-6 , 2)

# F = (-2 , 6)

# G = (-2 , 2)

- The vertices of Δ GHI are:

# I = (0 , 2)

# H = (-2 , 4)

# G = (-2 , 2)

- From the figure

∵ Point I is in the opposite side of the vertical line x = -2

∵ Point I in ΔGHI is corresponding to point E in Δ GFE

∴ G'H'I' is the image of Δ GHI by reflection across the line x = -2

∴ Its vertices must be

# I = (-4 , 2)

# H = (-2 , 4)

# G = (-2 , 2)

- Find the length of the side H'G' by subtracting the y-coordinates

 of points H' and G' and find the length of side FG by subtracting

 the y-coordinates of points F and G

∵ The length of the side H'G' is 2 units ⇒ (4 - 2 = 2)

∵ The length of the side FG is 4 units ⇒ (6 - 2 = 4)

∵ FG/H'G' = 4/2 = 2

∴ Δ G'H'I' dilated by scale factor 2 and center G to get Δ GFE

∴ There is a constant ratio between the sides of Δ G'H'I' and Δ DFE

- Triangles are similar if their corresponding sides are proportion

∴ Δ G'H'I' similar to Δ DFE

- Reflection doesn't change the size of the figure

∵ Δ G'H'I' is congruent to Δ GHI

∴ Δ GHI  similar to Δ DFE

* The set of transformation would prove ΔEFG ~ ΔGHI is "Reflect

 ΔGHI over x = −2, and dilate ΔG′H′I′ by a scale factor of 2 from

 point G"

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )