[Lex Computer & Tech Group/LCTG] Re. AI as a visual geometry problem solver

Sun Feb 22 13:21:46 PST 2026

I assumed the tick marks indicate that the two lines, for the left 
triangle, are identical in length resulting in an isosceles triangle. If 
so, and assuming the presented diagram is planar, the bisection of the 
vertical line with the horizontal line does not yield 90 degree angles 
for the two inner triangles, which is the way they appeared to me as I 
looked at the figure (and it also appeared to me that the horizontal 
line was straight). From the isosceles triangle perspective😉, x =  20 
degrees. From the 90 degree angle perspective, x = 30 degrees. Both 
answers were given as possible options. To me, the primary assumption 
that must be made is to assess the angle(s) at the vertical/horizontal 
intersection.

I still don't think enough information was given in the problem to 
establish a clear conclusion for this assumption. Thus, I maintain the 
problem is faulty.

Probably not worth further contemplation as we encounter the approaching 
blizzard. I can't wait!😇

-Dick

On 2/22/2026 3:00 AM, Robert Primak via LCTG wrote:
> Let's not overthink this one. The diagram could also be using 
> non-Euclidian geometry.
>
> But I'm thinking the problem is from a high school geometry test, so 
> that it would not be correct to assume anything other than planar, 
> Euclidian geometry, and not a projection of any kind. I missed the 
> significance of the tick marks, which make it impossible for the 
> "vertical" line to be in fact truly vertical. The angles are indeed 
> 80-degrees and 100-degrees, making solving for the top angles trivial. 
> I drew the scaled model to convince myself that this is a correct 
> interpretation.
>
> -- Bob Primak
>
>
> On Saturday, February 21, 2026 at 06:51:05 PM EST, Jon Dreyer via LCTG 
> <lctg at lists.toku.us> wrote:
>
>
> Surely we can stretch the problem in all sorts of ways: maybe it's not 
> planar, maybe apparently straight lines aren't straight, maybe it's on 
> the surface of a sphere, maybe the x is a Roman numeral 10, etc. But 
> there is a fairly standard language of geometry diagrams. Typically, 
> geometry diagrams are assumed planar unless we're told otherwise, and 
> lines that appear straight are assumed straight unless we're told 
> otherwise. But angles that look right cannot be assumed to be right 
> angles unless they have that little right-angle-indicator square at 
> the vertex.
>
> So according to this fairly standard interpretation, there's only one 
> right answer. Of course the problem is (probably intentionally) 
> misleading because the 80° angle does look closer to 90°.
>
> -
>
> Jon Dreyer
> Math Tutor/Computer Science Tutor <http://www.passionatelycurious.com>
> Jon Dreyer Music <http://music.jondreyer.com>
>
> On 2/21/26 17:28, Richard Wagner via LCTG wrote:
>
> Just saw this emailed problem and accompanying thread, etc. I am in 
> Bob's corner to the extent that the problem is not simple. Not enough 
> information is given in the problem and assumptions must be made where 
> different assumptions can be correct!
>
> Is the object planar or are we seeing a 3D projection of it. If the 
> latter, are we viewing it where one side is planar from our vantage? 
> If the right side is planar to us, then the answer is 30 degrees from 
> the law of sum of angles in a triangle and the angle at the bisection 
> of the vertical line and horizontal line _appears_ to be  90 degrees. 
> (From the Pythagorean Theorem {a squared + b squared = c squared}, the 
> ratio of the sides is 1:square root of 3:2 for opposite sides of a 
> 30:60:90 degree triangle. I'll never forget this ratio and formula 
> from high school /ad nauseam)./ If we're seeing the left triangle as a 
> planar projection of a 3D object, the angle of the left triangle at 
> the vertical/horizontal bisection must be 80 degrees for the given 
> isosceles triangle. This leaves the angle on the other side of this 
> bisection open to question. Naively, one would assume it to be 100 
> degrees, if one assumes the "horizontal" line to be straight, and x to 
> therefore be 20 degrees. However, one can't assume the bottom line to 
> be horizontal if the object is a projection, and from the information 
> given we can't determine angle at the vertical/horizontal bisection 
> for the triangle on the right side of the projection.
>
> Thus, I think the problem is unsolvable from the information given, 
> and I'm not surprised that AI is confused and gave conflicting 
> results. I agree with Olga: be cognizant to what AI is doing and don't 
> summarily assume it is giving correct answers to your queries and 
> conversations.
>
> -Dick
>
> -
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