The 10 Greatest Triangles of the 21st Century (So Far)
A pop-culture countdown of triangles: 20-99-101, the SSA ambiguous case, 3-4-5 with inradius 1, the obtuse 5-12-14, a spherical triangle with three right angles, the self-congruence proof of the isosceles theorem, the equilateral, 8-15-17 and the 45-45-90.
Content note: 'ASS-es' pun (SSA).
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-10-08-the-10-greatest-triangles-of-the-21st-century/ (CC BY-NC 4.0)Transcript
[Cover] "Math with Bad Drawings presents The 10 Greatest Triangles of the 21st Century (So Far)"
#10: The 20-99-101. "Some call it a mere base-ten novelty. Others, an enduring classic. Hey, why not both?"
#9 and #8: The Ambiguous Pair. [two triangles with a 30° angle and sides 10 and 6] "Same Angle. Same Side. Same Side. And yet… Love 'em or hate 'em, these rascals made ASS-es of us all."
#7: The 3-4-5. "Long derided as 'overrated,' 'overplayed' and 'interesting more for number theoretic properties than geometric ones,' this stalwart has a trick up its sleeve: an incircle whose radius is precisely 1. Let the haters chew on *that.*"
#6: The 5-12-14. "Is it right? No. Wrong? Perhaps. Either way, being obtuse never felt so good."
#5: The Triangle with Three Right Angles. [on a sphere] "Hello, Mr. Euclid? There's a sphere I'd like you to meet…"
#4: The triangle proved isosceles by its congruence to itself. "As angle B = angle C, we deduce △ABC is congruent to △ACB by AAS, and thus AB = AC. One of the first proofs found by computer. A harbinger of things to come."
#3: The Equilateral. "Beloved, reviled, canceled, resurrected, debated… and 2500 years after Plato, still dominating the conversation."
#2: The 8-15-17. "Too long overlooked in favor of the overrated 7-24-25, this Pythagorean gem is finally getting the love it has always deserved."
#1: The Isosceles Right. "As existentially terrifying as an irrational number, yet as friendly and familiar as a grilled cheese sandwich, it is the defining triangle of our time."