Question

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?

III, IV, II, I

IV, III, I, II

III, IV, I, II

IV, III, II, I

Answer 1

Sorry, but this would take too much time to explain.

Answer 2

You might find this useful to understand the theorem and its proof, not sure if its the same proof

http://telliott99.blogspot.com/2010/04/cevas-theorem-and-altitude-problem.html

Answer 3

@jim_thompson5910

Answer 4

it looks like statement II relies on statement I

Answer 5

since statement I says that BGCH is a parallelogram and then you use the properties of a parallelogram to show that the diagonals bisect each other to prove statement II

Answer 6

do you see how I'm getting all this?

Answer 7

yeah, i think so..

Answer 8

so because of this, this means that statement I must come first

Answer 9

so you can get rid of answer choices that have II, I in them

Answer 10

okay

Answer 11

b?

Answer 12

yes that's what I'm thinking. Statement III looks like its substituting values in what statement IV sets up

so IV needs to come before III

Answer 13

Okay! thank you. can you check this for me?

Answer 14

choice A is not correct because that is NOT a flaw in the proof

the slopes of the two segments are both 0 (and that is 100% true)

Answer 15

Oh :/ b?

Answer 16

what makes you say that?

Answer 17

I just guessed honestly..

Answer 18

try eliminating options you know aren't the answer

Answer 19

is choice D a flaw?

can she construct a midpoint?

Answer 20

no?

Answer 21

she can't construct a midpoint?

Answer 22

no, she can

Answer 23

so that's not a flaw

so D is out

Answer 24

is choice C a flaw?

Answer 25

yes!

Answer 26

why