Select the correct answer.

given: ∆abc

prove: a midsegment of ∆abc is parallel to a side of ∆abc.

statement reason

1. define the vertices of ∆abc to have unique

points a(x1, y1), b(x2, y2), and c(x3, y3). given

2. let d be the midpoint of and e be the

midpoint of . defining midpoints

3.

definition of midpoints

4. slope of

slope of definition of slope

5. slope of = slope of transitive property of equality

6. definition of parallel lines

7. let f be the midpoint of . defining a midpoint

8. definition of midpoint

9. slope of

slope of definition of slope

10.

11. definition of parallel lines

12. similarly, is parallel to . steps similar to steps 1−11

what is the missing step in this proof?

a.

statement: slope of = slope of

reason: definition of slope

b.

statement: slope of = slope of

reason: transitive property of equality

c.

statement: df = bc

reason: corresponding sides of congruent triangles are congruent.

d.

statement: ∆adf ≅ ∆abc

reason: asa solve for 10