Which is the most logical order of statements and justifications i, ii, iii, and iv to complete the proof?

a iii, iv, ii, i
b iv, iii, i, ii
c iii, iv, i, ii
d iv, iii, ii, i

IV,III,I,II

Step-by-step explanation:

We are given that a triangle ABC in which three medians are given .

We are given  a proof of three medians of a  triangle which intersect at  common point.

We have to find which is the most logical order of statement and justifications I,II,III and IV to complete the proof.

Statement:Point F is the mid- point of segment AB and point E is the mid-point of segment AC.

Draw segment BE and draw segment FC.

Justification: By construction

Statement: Point G is the point of intersection of segment BC and segment FC.

Justification: Intersecting lines postulate

Statement:Draw  segment AG.

Justification: By construction

Statement:Point D is the mid- point of intersection between segment AG and segment BC.

Justification: Intersecting lines postulate

Statement:Point H lies on segment AG such that

Justification: By construction

Step:IV

Justification: Midpoint segment theorem

Step III.

Justification: Substitution

Step I.BGCH is parallelogram

Justification: By property of parallelogram (Opposite sides are parallel)

StepII:

Justification: Property of parallelogram (diagonals of parallelogram bisect each other)

Statement: AD is median

Justification: Definition of median

IV,III,I,II