Andrewas: Both larger shapes have a "run" of 13 squares and a "rise" of 5. Yet, we all agree the difference is found in the hyptenuse. If that line (the hypotenuse) has equivalent end-points, the only way the slope can vary is if one or both of them is curved. At least one of the lines is simply not straight.

[edit] Oh, and my statement that equal triangles *are* similar was made to disprove the assertion made by you that "all components are the same" which I took to mean you thought the triangles were equal but not similar.

[ 11-07-2002, 06:04 PM: Message edited by: Timber Loftis ]

Andrewas - thank you ....

Daveros - *bthththtlt* [img]tongue.gif[/img]

Thats right. It's not a straight line. It is actually two straight lines with an angle of apx 0 but not exactly 0. As andewas pointed out there is a vertex.

Okay, now I see where we misunderstood each other. The "curvature" I mentioned was regarding the single long hypotenuse of each shape. Now that you point out that this line is actually two lines, each of which is straight, I see we are in agreement. Thanks. PS - I don't think *any* mention of the "hypotenuse" on my part *ever* referred to the smaller red and green triangles, and that's perhaps why I was confusing folks.

Yeah, we all agree .... we were just nit picking on each others approach! And who started all of this by the way?!?! My head now hurts! Bubye! [img]tongue.gif[/img]

I agree with this statement 100%, as I've seen this geometrical puzzle before.

<font color = lightgreen>The leftmost angle in the green triangle has a measure of arctan .4 = 21.8 degrees.
The leftmost angle in the red triangle has a measure of arctan .375 = 20.56 degrees.

Take the first diagram, invert it, and slide it next to itself to create a rectangle. You would find that
there is a sliver whose area equals 1.

A wonderful problem to let your high school geometry students try to solve for a week. [img]graemlins/firedevil.gif[/img] </font>