Points for solving Geometry Problem

[FourLengthsClear]

Impossible Triangle

I will give 30 points to the poster with the first correct answer plus some bonus points* if the explanation is especially lucid.

* No rollover required!

[Kaabee]

the small green and large red triangles don't have the same slope

hypotenuse goes from concave to convex

[pattymayo]

The figures are neither congruent nor triangles. The triangle that is made from the three acute angles along the perimiter of the figure should have a hypotenuse with a slope of 5/13. The red triangle has a hypotenuse with a slope of 3/8, and the blue triangle has a slope of 2/5. The small triangles should have slope congruent to eachother and the triangle-ish figure they make, since they dont there is an obtuse angle along the hypotenuse of the triangle-like large figure, making it an irregular tetragon.

When you switch the red and blue triangles, it changes the concave obtuse angle into a convex obtuse angle, therefore changing the area. The missing square comes from the sliver that is changed along the hypotenuse.

[FourLengthsClear]

Well done guys!

[cant call it]

He has undeniable proof that the bermuda triangle is actually a parrallellogram.
Good luck.

[Kaabee]

thanks FLC

[trytrytry]

thread of the week

[dynamite140]

Ask Hawley. That kid does homework while visiting the forums.

[jstblaze]

but they are not triangles.

[NYSportsGuy210]

just by looking at it i kinda figured out that both triangle top and bottom were not equal.

So why did u say in the problem that they were?

[NYSportsGuy210]

Can someone tell me or clarify what this problem is supposed to test you for or show?

[FourLengthsClear]

just by looking at it i kinda figured out that both triangle top and bottom were not equal.

So why did u say in the problem that they were?

The four shapes/sections that make up the 'triangles' are identical in both diagrams.

[FourLengthsClear]

Can someone tell me or clarify what this problem is supposed to test you for or show?

It is a test of logic, really.

The proposition put forward is this:
Four sub-sections of identical area produce shapes of different areas when arranged in two different ways.

This is clearly impossible.

Given that the adjacent and opposite sides of the right-angled triangle are of the same length in both diagrams, there must be an issue/trick with the hypotenuse. The fact that they are not straight is somewhat masked by the red/green colours used.

[NYSportsGuy210]

Its like putting puzzle pieces tpgether as far ad Im concerned. If ypu have ever played Tetris before this isn't too hard of a problem. There is a cooler one on Yahoo! having to do with juxtaposing black and white squares and how the color pqttern can play tricks on ir eyes.

[jstblaze]

if they were actually "triangles" as said it wouldnt work.

thats why the question put forth was confusing a bit.

[FourLengthsClear]

if they were actually "triangles" as said it wouldnt work.

thats why the question put forth was confusing a bit.

Fair comment but it is difficult not to give too much away without using that word.

[JohnGalt2341]

Very cool. I won't be awarding any points for this but can anyone tell me how this picture is possible?

[FourLengthsClear]

Very cool. I won't be awarding any points for this but can anyone tell me how this picture is possible?

There are a few like that. It is two or three parts placed to look like a single structure when viewed from exactly that angle.

In the one you posted, what looks like the fron-right vertical 'post' is actually two pieces, same with the front-top horizontal 'strut'.

[baskets]

I love geometry.

[chilidog]

The figures are neither congruent nor triangles. The triangle that is made from the three acute angles along the perimiter of the figure should have a hypotenuse with a slope of 5/13. The red triangle has a hypotenuse with a slope of 3/8, and the blue triangle has a slope of 2/5. The small triangles should have slope congruent to eachother and the triangle-ish figure they make, since they dont there is an obtuse angle along the hypotenuse of the triangle-like large figure, making it an irregular tetragon.

When you switch the red and blue triangles, it changes the concave obtuse angle into a convex obtuse angle, therefore changing the area. The missing square comes from the sliver that is changed along the hypotenuse.

There is no blue triangle. You should've edited your copy/paste before posting it.

[JohnGalt2341]

There are a few like that. It is two or three parts placed to look like a single structure when viewed from exactly that angle. In the one you posted, what looks like the fron-right vertical 'post' is actually two pieces, same with the front-top horizontal 'strut'.

I do believe you are correct. Look at the picture below of a very similar structure. The video below the picture explains how it's done.

[8ArIvd5]

Are 2 triangles with different slopes exactly the same? it's like saying a right isosceles triangle is exactly like an equilateral triangle.

[FourLengthsClear]

A bit like the 'nuts' one is the spinning mask which will 'fool' your brain you no matter how many times you see it.



Even wierder, to my mind, is the McGurk effect though (I think I might have posted this once before).

[Dirty Sanchez]

the small green and large red triangles don't have the same slope

hypotenuse goes from concave to convex

[FourLengthsClear]

Are 2 triangles with different slopes exactly the same? it's like saying a right isosceles triangle is exactly like an equilateral triangle.

No-one said they were exactly the same only that they have the same components.

[NYSportsGuy210]

I don't get that McGurk effect jibberish. How can he possibly be saying "ba ba ba" in both instances when your mouth and voice automatically produce a "va va va" when your upper teeth scrape your bottom lip and you say "ba ba ba".

That is what and how the "v" sound is produced physically.

[FourLengthsClear]

I don't get that McGurk effect jibberish. How can he possibly be saying "ba ba ba" in both instances when your mouth and voice automatically produce a "va va va" when your upper teeth scrape your bottom lip and you say "ba ba ba".

That is what and how the "v" sound is produced physically.

Listen to the video with your eyes closed. Do you ever hear "va"?

[gryfyn1]

I don't get that McGurk effect jibberish. How can he possibly be saying "ba ba ba" in both instances when your mouth and voice automatically produce a "va va va" when your upper teeth scrape your bottom lip and you say "ba ba ba".

That is what and how the "v" sound is produced physically.

He is mouthing the "v" sound. but the sound track is playing "ba"

you're minds ability to assemble the massive amount of information it receives is vastly imperfect, and easily fooled.

In fact a vast majority of what you experience as reality is just a massive set a presumed assumptions your mind has developed and is attempting to wedge what is happening into.