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.


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 Const

Answer 1

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 BD ≅ Line segment DC

Properties of a Parallelogram (diagonals bisect each other)
III

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

Substitution
IV

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

Midsegment Theorem

Line segment AD is a median

Definition of a Median

Answer 2

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

Answer 3

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 4

this is the last nasty sucker for this worksheet :)

Answer 5

hey gane

Answer 6

any tips?

Answer 7

this is tough reading.

Answer 8

ahh

Answer 9

let me make it simpler

Answer 10

give me 5 minutes

Answer 11

k

Answer 12

Statements:
Point F is at midpoint of line segment AB.
Point E is a midpoint of line segment AC.
Draw line segment BE.
Draw line segment FC.

Answer 13

Justifications:
By construction.

Answer 14

Statements:
Point G is the point of intersection between
line segment BE and line segment FC.

Answer 15

Reasons:
Intersecting Lines Postulate

Answer 16

Statements:
Draw line segment AG.

Answer 17

Justifications: Intersecting Lines Postulate

Answer 18

Statements:
Point D is the point of
intersection between
like segment AG
and line segment BC.

Answer 19

opps

Answer 20

The Justification for the drawing of line segment AG was by construction

Answer 21

The Point D intersection one is Intersecting Lines Postulate

Answer 22

OK, I have a handle on this. But you are the one who is supposed to learn how to do it.

Answer 23

Point H lies on line segment AG
such that line segment AG
is congruent to line segment
GH.

Answer 24

can you teach me?

Answer 25

Justification:
By construction

Answer 26

I. BGCH is a parallelogram.

Answer 27

Justification:
Properties of a
Parallelogram(opposite sides are parallel)

Answer 28

II line segment BD is congruent to line segment DC

Answer 29

First, read I. it can't be first, because we haven't said anything about parallel lines.
read II
should it come before or after I ?

Answer 30

Justification:
Properties of Parallelograms
(diagonals bisect each other)

Answer 31

The one I just wrote was II.

Answer 32

Yes. now read I and II. which ones goes ahead of the other?

Answer 33

Lol, II goes before one

Answer 34

cause like you said, we haven't talked about parallel lines yet

Answer 35

II uses "properties of parallelograms"
that means you have to prove you have a parallelogram before you can use II

I goes ahead of II

Answer 36

III. Line segment GC is parallel to
line segment BH
Line segment BG is parallel to line segment
HC.

Answer 37

yep

Answer 38

Justification: Substitution

Answer 39

IV. line segment FG is parallel to line segment BH.
Line segment GE is parallel to line segment HC

Answer 40

Justification is the Midsegment Theory

Answer 41

III does prove parallel lines. So it comes before I

Answer 42

Line segment AD is a median

Answer 43

Because of Definition of a median

Answer 44

k

Answer 45

makes sense

Answer 46

you can stop typing the question.

Answer 47

So I is last obviously

Answer 48

what is the answer?

Answer 49

Because all of the other reasons have to support that the figure is a parallelogram

Answer 50

So we have narrowed it down to two options

Answer 51

IV, III, II, I or III, IV, II, I

Answer 52

no. but we can work backwards.

Answer 53

I has to be last

Answer 54

right?

Answer 55

In order to prove that the figure is a parallelogram

Answer 56

Because we do not whether its a parallelogram or not until we have used

reasons two, three, and four.

Answer 57

I kinda think III goes first

Answer 58

and IV goes second

Answer 59

no. we are trying to prove the 3 medians intersect. the first 2 are easy. the 3rd median goes from A to D. what statement claims: BD=DC (making D the midpoint).?

Answer 60

II. obviously

Answer 61

But it does not go first, either

Answer 62

It could only go last

Answer 63

ohhh

Answer 64

II is the last thing you do before saying AD is a median. So it goes last.

Answer 65

so II. is last

Answer 66

i see

Answer 67

It makes sense now

Answer 68

now what does II use for its justification?

Answer 69

And then 1. goes before II.

Answer 70

I.

Answer 71

I proves a parallelgram and II uses it. so we have ?,?,I, II
what is the justification for I?

Answer 72

hmm

Answer 73

I'm going with III.

Answer 74

Cause it proves about the parallel lines

Answer 75

so it has to go before I.

Answer 76

the justification for I is
Properties of a Parallelogram (opposite sides are parallel)

which statement concludes you have parallel lines?

Answer 77

III.

Answer 78

Like I said

Answer 79

It proves that the lines are parallel

Answer 80

so IV. would have to go at the beginning

Answer 81

and IV must go first.

Answer 82

yep

Answer 83

So it goes IV,III,I,II..?