Question

Point 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.
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
𝐷
𝐹
=
1
2
𝐵
𝐶
upper D upper F equals Start Fraction 1 over 2 End Fraction upper B upper C

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

DE=12AB
𝐷
𝐸
=
1
2
𝐴
𝐵
upper D upper E equals Start Fraction 1 over 2 End Fraction upper A upper B

BC=2EF

Answer 1

DF = 1/2 BC.

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