Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Possible Duplicate:
A parallelogram and a line joining a vertex to the midpoint of opposite side
Proving two lines trisects a line

$\rm ABCD$ is a parallelogram (in the plane) and $\rm E$ is the midpoint of $\rm AB.$ Prove that $ \rm AC$ and $\rm DE$ trisect one another. In other words, that their point of intersection $\rm X$ divides each of them in the ratio $2 : 1.$

share|improve this question

marked as duplicate by Phira, J. M., t.b., Henning Makholm, Did Oct 31 '11 at 13:35

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

3  
Welcome to math.stackexchange! Just so you get used to some of the etiquette on this site, I'll list some pointers =]. a) Don't ask questions in the imperative (often how they are given to you). Instead, phrase it like "Can someone please offer me some help on.." b) Show your working. This helps us know you are actually trying and that we are not just doing your homework for you, and also helps us pinpoint where to elaborate our answers. c) If this is homework, that's ok, we don't mind helping you. Just make sure you tag it homework (I've done it for you this time). Enjoy! –  Ragib Zaman Oct 19 '11 at 12:44
add comment

2 Answers

Hint: Do the triangles $\bigtriangleup{AXE}$ and $\bigtriangleup{CXD}$ have anything in common?

share|improve this answer
add comment

Medians of the triangle $ABD$ (see picture bellow) intersects in point $X$ and divide each other in ratio $2$:$1$ so we may write following:

$EX:DX=1:2$

$AX=\frac{2}{3}\frac{AC}{2}=\frac{AC}{3} , XF=\frac{1}{3}\frac{AC}{2}=\frac{AC}{6}$

Since diagonals of the parallelogram divide each other in ratio $1:1$ we may write:

$XC=XF+\frac{AC}{2}=\frac{AC}{6}+\frac{AC}{2}=\frac{2AC}{3}$ , so we may conclude:

$AX:XC=\frac{AC}{3}:\frac{2AC}{3}=1:2$

enter image description here

share|improve this answer
    
Ah thank you very much! –  Paul Oct 19 '11 at 15:52
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.