Question

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

Answer 1

I think its B IV,III, I, II

Answer 2

Answer:

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 $AG\cong GH$

Justification: By construction

Step:IV $FG\parallel BH,GE\parallel CH$

Justification: Midpoint segment theorem

Step III.$GC\parallel BH,BG\parallel CH$

Justification: Substitution

Step I.BGCH is parallelogram

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

StepII:$BD\cong DC$

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

Statement: AD is median

Justification: Definition of median

Answer:IV,III,I,II