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.

Answer 1

STATEMENTS:
1. Point F is a midpoint of AB
Point E is a midpoint of AC
Draw BE
Draw FC
2.Point G is the point of intersection between BE and FC
3. Draw AG
4. Point D is the point of intersection between AG and BC
5.Point H lies on AG such that AG ≅ GH
I . BD ≅DC
II. FG II BH and GE II HC
III. GC II BH and BG II HC
IV.BGCH is a parallelogram
6. AD is a median

Answer 2

posting justifactions and picture now too

Answer 3

Justifications:
1. By Construction
2. Intersecting lines postulate
3. By Construction
4. Intersecting line postulate
5. By Construction
I.Properties of a Parallelogram (diagonals bisect each other)
II.Midsegment Theorem
III. Substitution
IV.Properties of a Parallelogram (opposite sides are parallel)
6.Definition of a Median

Answer 4

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

II, III, I, IV

III, II, I, IV

II, III, IV, I

III, II, IV, I

Answer 5

Picture:

Answer 6

is this all one question or multiple ones?

Answer 7

One question

Answer 8

ok let me work on it for you.

Answer 9

Ok:D

Answer 10

II IV I III for the order question, I believe... hold on I'm still thinking about the rest

Answer 11

If your teacher is honestly giving you these questions, tell her to shut the hel* up.. god I hate these ones....

Answer 12

Haha, but its only one question aha

Answer 13

wait, II, IV, I, III isnt a answer?

Answer 14

All that is one quesiton

Answer 15

Im thinking out loud lol

Answer 16

ok this is confucing the heck outta me, but I am pretty sure parth will help you cause he is genius

Answer 17

confusing*

Answer 18

It was II, III, IV, I