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or,,prove that this ratio always equals 4/3

im watching :)

|dw:1350313254678:dw|

Yukky algebra....think, think...

|dw:1350318976709:dw|

|dw:1350319309051:dw|

|dw:1350319508249:dw|

152 is a quarter 123
-> 123/235 is 4/3
-> 143/362 is 4/3 as well

Think that's right...

why is 352 half of 362 ?

Median divides triangle area in half?

how is 35 a median ?

|dw:1350323581495:dw|

72 || 34 coz 72 is the midsegment

|dw:1350323706822:dw|

7824 is a parallelog gram,
now imagine we translate it down

|dw:1350323784808:dw|

Yes, sorry, I didn't make the construction very clear.......

it translates to 1672

why will 87 meet 6 ?

diagonals bisect each other in ||gram

so 65=52

87 meets at 6 becoz,
47 is congruent to 26,
42 is congruent to 21

the only tricky part in this proof i see is proving this :
326 is the triangle made by medians

i still dont get 876 thing..

ok did u get estudier diagram

yep..i followed every bit till now..

he constructed,
26 \(\cong\) 47

yes..

ahh alright,,so 36 isnt a median yet..okay,,

assume it is a median so that we prove the thing at hand, :)

alright,,

72 || 84, agree ?

yes..

becoz 72 is the midsegment

yes,,i could figure out..

7284 is a ||gram i have constructed

7248*

yes,,clear till now..

also, 74 congruent to 62, by construction

okay,,7426 is a //gm..

now imagine we slide the ||gram 7248 along the side 41

so you're saying those 2 //gms are congruent..

the diagonal in the ||gram 7248 translated to where ?

coincides with 62

|dw:1350324847401:dw|

the diagonal 74 coincides wid 62
the side 42 coincides wid 21

yes,,the 2 //gms are congruent..

|dw:1350324939445:dw|

7248 congruent 6127

we just use this : 6127 is a ||gram
that gives 5 is midpoint of diagonal 62

that one we already knew right ?

which one ? i thought we're trying to prove 5 is midpoint of 62 lol

whats ur question

no

??

those 2 became congruent || grams by construction, 5 got nothing to do wid it

let me put everything in one reply

ok if that make sense good :)

so only assumption we need to prove is 36 is a median, right ?

yep..

excellency yet again..!! thank you @sauravshakya

and big thank you to @ganeshie8 ..your idea was used here after all..

+ @estudier you sparked the figure, ofcourse ! :P

I managed to get an outline of this just with algebra --- what a mess!!