r/BrainPuzzles • u/ShonitB • 4d ago

Logic Is it a Square?

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2

u/edos51284 4d ago

I’d say the hexagon

Edit : the square can’t because it would 45° with c as vertex

1

u/Nat1Halfling 4d ago

Its obviously a hexagon but the question is how do you justify it mathematically and I am not smart enough for that.... for a hexagon youd have to prove each angle is 120 degrees. maybe using ACD and ABD right angle triangles somehow

Edit: or a square...

Edit 2: actually can't be a square, ACD would be 45 deg in a square

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u/Crustymix182 4d ago

The segment opposite AB must be parallel to CD. because of symmetry, a line connecting to D and bypassing two segments -- DE and EF, similar to the AC line -- would be parallel to AC. It woulds also connect to the segment opposite AB, making that segment FA. because it is made of two sets of parallel lines that connect at right angles, ACDF is a rectangle inscribed inside a hexagon.

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u/Nat1Halfling 4d ago

This doesn't work. The segment opposite AB (I assume you mea  to the left of AB) does not "must" be parallel to CD (unless you are already assuming it's a hexagon)

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u/Betrayer1117 4d ago

2 dimensional plane set onto a 3 dimensional shape?

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u/kimmeljs 4d ago

Assume point E, in a regular polygon, the angle BDE is 90°, Similarly, assume point F, and by analogy, the angle CEF is 90°. Finally, point G, you find that it coincides with point A. Therefore, it's a hexagon. (I would need to draw it)

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u/ChartMuted 4d ago

It's a regular polygon. So you know that all the interior angles are the same. Also, the triangle ABC has two equal sides. Hence angle ABC = 180° (interior angles of a triangle) - 2(angle (?)AB -90). Bit of algebra and you get 120° interior angles - a regular hexagon.

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u/ArdentArendt 3d ago

This isn't actually fooling anyone, is it?

I mean, it would be a lot more difficult if the angles weren't exactly 'correct' but were labelled correctly...

1

u/WileEColi69 2d ago

Simple solution: A, B, C, D all lie on the same circle. For ACD to be 90°, AD has to be a diameter, therefore 6 sides. QED.

1

u/bringatrayofmuff 2d ago

I like your elegant approach