Question

Use ∆ABC to answer the question that follows.

Given: ∆ABC

Prove: The three medians of ∆ABC intersect at a common point.

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point.


Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?

Answer 1

Statements

Justifications

Point F is a midpoint of Line segment AB
Point E is a midpoint of Line segment AC
Draw Line segment BE
Draw Line segment FC

by Construction

Point G is the point of intersection between Line segment BE and Line segment FC

Intersecting Lines Postulate

Draw Line segment AG

by Construction

Point D is the point of intersection between Line segment AG and Line segment BC

Intersecting Lines Postulate

Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH

by Construction
I

BGCH is a parallelogram

Properties of a Parallelogram (opposite sides are parallel)
II

Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC

Midsegment Theorem
III

Line segment BD ≅ Line segment DC

Properties of a Parallelogram (diagonals bisect each other)
IV

Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC

Substitution

Line segment AD is a median

Definition of a Median

Answer 2

IV, II, III, I

II, IV, I, III

IV, II, I, III

II, IV, III, I

Answer 3

It won't let me post the statements and justification in a two column

Answer 4

try taking a screenshot and post the pix... here you're trying to use parallelogram properties i think

Answer 5

I just did.

Answer 6

Does this work?

Answer 7

look at \(\triangle ABH\)

Answer 8

Just heads up I HAVE NO CLUE what I'm doing.

Answer 9

FG is the midsegment , so it is parallel to BH

FG || BH

Answer 10

ok

Answer 11

its okay im sure you would get enough clue by the time we finish ;p

Answer 12

Alright, continue.

Answer 13

do the same thing for another triangle,

look at \(\triangle\) AHC

whats the midsegment in that triangle

Answer 14

EB

Answer 15

?

Answer 16

No EG?