Question

Use the image to answer the question.

A triangle is marked clockwise from the lower left vertex as upper A upper B upper C. Point upper D is marked at the midpoint of side upper A upper B. Point upper F is marked at the midpoint of side upper A upper C.

Opal has already proved that △ADF∼△ABC
. They are now attempting to prove that DF=12BC
and DF¯¯¯¯¯¯¯¯∥BC¯¯¯¯¯¯¯¯
. Critique their reasoning. Which option should fill in the blank?

PROOF: Because corresponding sides of similar triangles are proportional, ________________Blank. Multiply both sides of the equation by segment BC
to show that DF=12BC
. Because corresponding angles of similar triangles are congruent, ∠ADF≅∠ABC
. If corresponding angles are congruent, then lines are parallel, so DF¯¯¯¯¯¯¯¯∥BC¯¯¯¯¯¯¯¯
.

(1 point)
Responses

BCDF=2
Start Fraction upper B upper C over upper D upper F End Fraction equals 2

AD=DB
upper A upper D equals upper D upper B

DFBC=12
Start Fraction upper D upper F over upper B upper C End Fraction equals Start Fraction 1 over 2 End Fraction

DF=BC

Answer 1

Start Fraction DF over BC End Fraction = Start Fraction 1 over 2 End Fraction (i.e. DF/BC = 1/2).