Sergei wants to prove that triangle abc is similar to triangle fgh which would him prove that? check all that apply. a.) measure angles a and f to show they are congruent. b.) measure angles f and g to show they are congruent. c.) use the right angle marks to show that angles c and h are congruent. d.) use the grid or a ruler to show that ab = fg, bc=fg, and ac=fh. e.) use the grid or a ruler to show that fg/ab = gh/bc = fh/ac.

Option (A) and (E) are correct.

We can prove  ΔABC and ΔFGH  are similar by AA criterion or by showing that the  ratio of corresponding sides are equal.

Step-by-step explanation:

Given : two triangles, ΔABC and ΔFGH and we need to prove both are similar to each other.

We have to choose the correct options from the given choices.

 Two triangles are said to be similar if their the corresponding sides are in proportion and the corresponding angles are congruent to each other.

 that is

also measure ∠A and  ∠F  to show they are congruent as ∠H= ∠C = 90°

This can be observed by looking at the image . So when both triangle are congruent we an show by AA similarity criterion that  ΔABC and ΔFGH  are similar.

Thus, option (A) and (E) are correct.

We can prove  ΔABC and ΔFGH  are similar by AA criterion or by showing that the  ratio of corresponding sides are equal.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.