Question

Use the image to answer the question.

A triangle is labeled clockwise as upper A upper B upper C from the upper left vertex. Another triangle upper D upper E upper F is drawn inside the first triangle.
▶Click for Long Desc

Image Long DescriptionPoint upper D is marked at the midpoint of side upper A upper B. Segments upper A upper D and upper D upper B are marked with single congruent tick marks. Point upper E is marked at the midpoint of side upper B upper C. Segments upper B upper E and upper E upper C have congruent triple tick marks. Point upper F is marked at the midpoint of side upper A upper C. Segment upper A upper F and upper F upper C have congruent double tick marks. Three lines connect midpoints upper D to upper E, upper D to upper F, and upper F to upper E, forming a second triangle.

Given the image, which statement must be true?

(1 point)
Responses

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

2DF=AC
2 upper D upper F equals upper A upper C

BC=2EF
cap b cap c is equal to 2 cap e cap f

DE=12AB

Answer 1

DF = 1/2 BC.

Reason: D and F are midpoints of AB and AC, so DF is a midsegment of triangle ABC. A midsegment is parallel to the third side and half its length, so DF = (1/2) BC.