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

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

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

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

Start Fraction upper A upper B over upper B upper C End Fraction equals Start Fraction upper A upper C over upper D upper F End Fraction equals Start Fraction upper D upper E over upper E upper F End Fraction

Answer 1

Option 3.

Reason: The right angles correspond (B ↔ E) and the θ angles correspond (C ↔ F), so A ↔ D. Therefore corresponding sides are AB ↔ DE, BC ↔ EF, and AC ↔ DF, giving AB/DE = BC/EF = AC/DF.