Triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'. On a coordinate plane, (0, 0) is the center of dilation. Triangle FDE is dilated to create smaller triangle F prime D prime E prime. Triangle FDE has points (- 9, 3), (- 9, 9), (- 6, 6). Triangle F prime D prime E prime has points (- 3, 1), (- 3, 3), and (- 2, 2). Which statements are true?A. ∠F corresponds to ∠F'. B. Segment EE' is parallel to segment FF'. C. The distance from point D' to the origin is One-third the distance of point D to the origin. D. The measure of ∠E' is One-third the measure of ∠E. E. △DEF △D'E'F'.

a) True.

b) False.

c) True.

d) False.

e) True.

Step-by-step explanation:

A. ∠F corresponds to ∠F'.  True.

B. Segment EE' is parallel to segment FF'.  False. They intersect each other at the origin.

C. The distance from point D' to the origin is One-third the distance of point D to the origin.   True.

We can get the ratio D'E'/DE:

D. The measure of ∠E' is One-third the measure of ∠E. False.

E. △DEF ~ △D'E'F'. True. They are similar triangles.

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet