Question

Use the image shown below to answer the question that follows.

The two-column proof below proves the following theorem: The three medians of a triangle all intersect in one point.
Statements

Reasons

Point F is a midpoint of

Point E is a midpoint of

Draw

Draw

By Construction

Point G is the point of intersection between and

Intersecting Lines Postulate

Draw

By Construction

Point D is the point of intersection between and



Point H lies on such that

By Construction

and

Midsegment Theorem

and

Substitution

BCGH is a para

Answer 1

ignore the weird part im gonna retype it

Answer 2

@jim_thompson5910

Answer 3

@Hero

Answer 4

@UnkleRhaukus

Answer 5

@jim_thompson5910

Answer 6

ayudame

Answer 7

so you just want to fill in that empty reason?

Answer 8

yeah heres the options By Construction

Properties of a Parallelogram

Midsegment Theorem

Intersecting Lines Postulate

Answer 9

which one do you think it is

Answer 10

i know it isnt by construction

Answer 11

wait

Answer 12

hold on

Answer 13

ok

Answer 14

how is point D an intersection for segment AG when it doesnt extend to d

Answer 15

good thinking, but AG is NOT a segment when they write



it's actually a line

Answer 16

so they are saying it does expand past the d?

Answer 17

yes it extends infinitely in both directions

Answer 18

well in a sense that was constructed

Answer 19

what you construct is what you draw with a pencil, straightedge and compass

Answer 20

can you just plot D anywhere you like?

Answer 21

if you could, then you'd be creating the point D by construction

Answer 22

ok so i guess that isnt what they are looking for...i guess the intersecting lines postulate would make sense..it's simple but it works

Answer 23

and that's the correct answer, to make sure that point D is on both lines, you would just intersect them

Answer 24

that locks D in so to speak to that one spot only

Answer 25

ok thanks

Answer 26

The answer is (Intersecting Lines Postulate)