Question

Both triangles have an angle with a theta symbol, which is an oval with a horizontal line across the middle. All vertices are marked with closed points. Triangle upper A upper B upper C’s right-angle symbol is on the bottom left. The vertex is labeled upper B. The vertical, left leg is upper B upper A. The hypotenuse, which slopes downward from left to right is upper A upper C. The base is upper C upper B. The theta symbol is on the bottom right within vertex upper C. Triangle upper D upper E upper F sits on a tip, vertex upper D. The right-angle symbol is on the left and is labeled upper E. The left leg, upper E upper F, slopes upward, left to right. The hypotenuse, upper F upper D, slopes downward, slanting slightly right to left. Upper D upper E slants upward, right to left. The theta symbol is in the top angle, within vertex upper F.Determine which of the following ratios is correct. (1 point) Responses ABEF=BCDF=ACDE 𝐴 𝐵 𝐸 𝐹 = 𝐵 𝐶 𝐷 𝐹 = 𝐴 𝐶 𝐷 𝐸 Start Fraction upper A upper B over upper E upper F End Fraction equals Start Fraction upper B upper C over upper D upper F End Fraction equals Start Fraction upper A upper C over upper D upper E End Fraction ABDF=BCEF=ACDE 𝐴 𝐵 𝐷 𝐹 = 𝐵 𝐶 𝐸 𝐹 = 𝐴 𝐶 𝐷 𝐸 Start Fraction upper A upper B over upper D upper F End Fraction equals Start Fraction upper B upper C over upper E upper F End Fraction equals Start Fraction upper A upper C over upper D upper E End Fraction ABDE=BCEF=ACDF 𝐴 𝐵 𝐷 𝐸 = 𝐵 𝐶 𝐸 𝐹 = 𝐴 𝐶 𝐷 𝐹 Start Fraction upper A upper B over upper D upper E End Fraction equals Start Fraction upper B upper C over upper E upper F End Fraction equals Start Fraction upper A upper C over upper D upper F End Fraction ABBC=ACDF=DEEF

Answer 1

Triangles ABC and DEF are similar (each has a right angle and the same acute angle θ), so A↔D, B↔E, C↔F. Thus corresponding sides give

AB/DE = BC/EF = AC/DF.

This is option 3 (ABDE = BCEF = ACDF).