Help with two column proof of a trapezoid

I have been asked to do a two column proof for a trapezoid. I am stumped on what to do. I am homeschooled and I am using a tough curriculum so the book I have for geometry assumes you know how to do everything or figure it out on your own. I would really appriciate some help please!!

figure,

http://www.edusolution.com/regentsex...ler/ques33.gif

question: Given: ROSE is a trapezoid with bases OS and RE.

Prove, OI • RI = EI • SI

and this is supposed to be a two column proof. :)

Thank you very very much!!

two column proof of a trapezoid

Quote:

Originally Posted by

**Archie Meade** You could begin by saying that the areas of triangles OSR and SOE are equal

as they have the same base and perpendicular heights.

This means that triangles OIR and SIE also have equal areas as they differ from the above-mentioned triangles

by the area of triangle OIS.

Now write the area of the triangle OIR using the angle at I

$\displaystyle Area\ OIR=\frac{1}{2}|OI||IR|Sin(OIR)$

Do the same for triangle SIE

$\displaystyle Area\ SIE=\frac{1}{2}|SI||IE|Sin(SIE)$

However, those angles are identical.

Hence the result follows

Hello Archie and Minniemouse 2,

Archieyour proof is based on trigonometry and I believe would not be expected of a geometry student. It is aproblem involving parallel lines, transversals, equal angles and similar triangles.

Minnie if you do not understand these clues ask for more help.

bjh