Summer of Math Exposition

An important and very basic but often neglected topic! The idea of just “playing around” to figure out which trios of data suffice to determine a triangle (and why we need three) is very good. I do that, too, when I teach trigonometry. The video is very well made, though I think the (very nice-looking!) program may bring a little too much heavy artillery to this small struggle. It may give students the idea that fancy tech is needed to think about this sort of thing geometrically, which, of course, isn’t true at all. Still, I enjoyed the video, and the main lesson of getting students to think about determining data for a triangle is well motivated and presented.

Great job! The framing of “how to name a triangle” is a nice way to represent the concept of uniquely defining triangles with certain given information, and I think the idea of congruence rules relating back to triangles being uniquely defined is important and under-explained. There are naturally some loose ends you didn’t delve into with things like ASA or AAS, but I understand that to be a stylistic choice. (I do have to say, I would recommend being slightly more careful with patterns of four rotated copies of a right angle… naturally I don’t expect that was intentional, but something to keep an eye out for.)

Keep up the good work! And have a nice rest of your day

Using software that is easier to use

Visual on the different triangles on the single parameter case, if the sides of different triangles were different colours, it would help to pick it up a bit better.

I might suggest giving a bit more space for exercises when highlighting things to reader near the middle section. Gives them a bit more time to think and do the work on their own.

What’s the motivation as a high schooler to study this? It is interesting puzzle. I think it’s a pretty interesting view of congruence I have not thought of as uniquely specifying the triangle. I think this point can be highlighted a bit more because that’s actually what’s really interesting.

While I personally enjoyed seeing Paperland used for the explanations, it mght be a bit much for people who are not familiar with coding.

Not very novel, but appreciate the effort. The introduction got me hooked but you covered very basic math, maybe could’ve tagged this under middle school i suppose?

Beautiful explanation. It was a simple topic but the way of exploring why different ways don’t work and in that process, arriving at SAS congruence can be a very nice way of teaching students why it is used. Brilliant 👏

I really enjoy how interactive this video is. Encouraging the watchers to go out and explore it together is very cool.

This is a quick little video about triangles. For me, it’s nothing outright novel or memorable, but I see the motivation behind the video and it’s very clear and easy to follow.

I like that I could remake everything you’ve done in the video since you’ve shown every step with explanations and because the “Paperland” website is easily accessible. This makes experimentation easy and fun.

Great geometric visualizations of triangles, effective at demonstration. The justification about why “ASS” congruency does not work is very insightful: most materials do not dig into why and the conditions in which “ASS” does not work and leaves us to take it for granted. The video’s relevance can be further expanded upon if the formal concepts of similarity and congruence can be introduced, connected, and differentiated. Also, neat observation: “SAS” works because the third side is strictly bound by the Cosine Rule.