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dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Geometry Proof-HELP ASAP!!

In triangle ABC, the medians AD,BE, and CF concur at the centroid G. 
(a) Prove that AD < (AB + AC)/2. 
(b) Let P=AB+AC+BC be the perimeter of triangle ABC. Prove that 3P/4 < AD + BE + CF < P.

Please help asap!  Include solution too. Thank you!

Last edited by dazzle1230 (2016-05-17 13:29:45)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof-HELP ASAP!!

I feel I should give only hint.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Geometry Proof-HELP ASAP!!

would we need to use median ratios?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof-HELP ASAP!!

Yes. AG=2/3*AD etc.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Geometry Proof-HELP ASAP!!

i still cant seem to get Q3 part b.
I created tons of inequalities and put them in terms of other lines.
Then I added some of the inequalities together and I couldn't get the rest

apsara123

Member

Registered: 2016-05-14

Posts: 20

Re: Geometry Proof-HELP ASAP!!

Are you in sseraj's geometry class, because i have the same geometry question?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry Proof-HELP ASAP!!

hi guys,

This problem can be done by using the 'triangle inequalty'.  If x, y and z are the sides of any triangle then x < y + z

THis is an outline of what I did:

(a) AD < AB + BD

Write another expression for AD and add them together.

(b)  You can get one half of the inequality by using the first part.  Write two more expressions like this for BE and CF.  Then add them together.

Then AB < BG + AG and similar expressions for BC and AC.  Add these together and also use 3BG = 2BG and two similar.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof-HELP ASAP!!

Are you in sseraj's geometry class, because i have the same geometry question?

sseraj's classes where? Bengaluru or Chennai ?

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Geometry Proof-HELP ASAP!!

nvm, i found out how to do it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof-HELP ASAP!!

In what?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof-HELP ASAP!!

How can I use the centroid to prove that 3P/4<AD+BE+CF?

It is shown in some other thread probably started by apsara123.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof-HELP ASAP!!

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}