3 Different Types of Triangle Choke
The triangle choke is a huge part of jiu jitsu; whether from an offensive or a defensive standpoint, you're going to be dealing with it from day one. However, there are plenty of nuances to be explored revolving around the simple concept of making a triangle with your legs, and choking a person with their arm and head inside the "triangle." Not only are there dozens (perhaps hundreds) of unique set ups, there are also several different effective chokes you can learn and become proficient in.
The Reverse Triangle
The "reverse triangle" isn't simply switching your legs (the way they are figure-four'd), but instead, a completely new angle for the choke. Keep in mind that, no matter what, both carotid arteries should be cut off for the triangle to be optimally effective. Here, start from the mount position, trying for a reverse armbar. When you can't get the tap from the armlock, drive your knee over your partner's biceps, and let your foot swivel over, so that you are in something akin to a mounted triangle. However, drive your knee under their head, essentially reversing the direction in which you'd turn to finish a traditional mounted triangle. Prop their head up, similar to the way you'd do in S-mount. If you're attacking their right arm, it's your left knee that will drive under their head. From here, it's all about rotating so that you can swivel around to your opponent's back, triangling them from behind. The crook of your knee should be at the front of their face.
Judo players know of this triangle, a much more traditional version of "sankaku" often used to facilitate a pin. Here, we are, of course, interested in the submission. This opportunity often arises when you are trying to finish an armbar, and you notice that your foot is stuck under your partner's armpit, not over on top of their shoulder. This will often occur during a spinning armbar attempt. Assuming you are attacking your partner's left arm, switch to a Kimura grip, and then allow your left leg to retract off of your partner's torso. The general idea now is to bait your partner into starting to come up on top, and then sliding your left leg completely behind your partner's neck (not their back!). Once here, you can set up a tight figure four triangle, and simply squeeze your knees together for the finish. A similar triangle arises from the crucifix position.
Of course, facing your partner and submitting them with a triangle choke from guard (or mount, occasionally) is the most common occurrence of all leg triangles. The general idea here is to catch your partner's head and arm in between your legs, and then to bring their own arm across their throat, so their own shoulder cuts off one carotid, and your other leg (hamstring in particular) cuts off their other carotid. Pay particular attention to where the crook of your knee is, and make sure your knee is elevated higher than your foot for maximum constriction of blood flow to the brain.
Favorite type of triangle?
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Hopefully these three variations give you pause to think about some of the other possibilities that might be out there -- not only from the triangle choke position, but across all other positions. Any technique in Brazilian Jiu Jitsu has certain fundamental components that absolutely must be present in order for the move to work correctly, but the beauty and the innovation arises when we realize that there are many, many ways to make these components work, as evidenced by the half dozen different types of straight armlocks proliferating currently, or these triangle choke variations (all fundamentally the same concept!). Experiment, and come up with your own variations as your confidence level and experience rises. As always, let me know if these moves work for you!