F
We use this system, but asking which angles are the same when they are marked like this isn't testing the concept I'm getting at.
It's called "decoration" or "tic marks" and the little marks on the sides of the original triangle I posted are a part of the same system.
I would expect a student to mark the angles like this based on the way the sides are marked. My struggling student would make the wrong two the same.
@Bumblefish @3TomatoesShort @EverydayMoggie
This is a very deep mathematical question in a way. Why do we do geometric constructions with a "straight edge" and compass and not a ruler and compass?
@Bumblefish @3TomatoesShort @EverydayMoggie
Rulers are less precise than a compass. You could use a ruler if you wanted. But it will only be as precise as the markings you have made on the ruler.
Absolutely. If I had 30 students I would not do the compass work. And that would be a big loss, but I would not be able to go around the room and help enough of them to hold it correctly, and keeping that many compasses sharp and ready to go is too much work.
Likewise teaching them to sharpen the lead on the compass is too much of a class time-sink. (although it's a very cool skill to have)
I bring only working compasses with sharp lead to class.
Well then you are making triangles in a different plane or triangular prisms maybe.
Also different populations of students have different needs. So, maybe I would switch if I thought it would work better with a new group.
I make a big deal about introducing the Greek letters in the spring when we start trig. This gives them time to learn how to write them.
So they do learn them by the end of the year? New symbols are a big deal and deserve space. Don't just spring them on people. I do find the numbers a little "janky" from a pure maths lens.
The three letters eg ∠ABC where B is the vertex are also what I learned and I hated the numbers when I first saw them. But, from experience I find they just work better. My little grumble about "but numbers are for measuring" and also "that's not how I learned it" are something I've gotten past.
I go with what helps the most students get it. Hence I don't use greek letters with ninth graders. Learning the new symbols at the same time was too much for some.
@dahukanna
1 and 2 are totally correct.
An equilateral triangle is kind of isosceles triangle. One that works in three ways.
A line is a degenerate isosceles triangle with two right angles and a zero angle at the vertex OR two zero angels at the base and a 180 angle at the vertex. Probably better to call it a line.
Both of these are not always called isosceles but they are the natural extremes.
Using color to identify angles means you can't use it to show which ones are the same. Which is a great use for color if you don't have color blind students. (I don't at the moment but it's always in the back of my mind. )
That is too much second guessing. I mean... it's correct. I didn't say what kind of geometry or if this is on a plane. But ... that's too much.
That's interesting. I *also* have no sense of left or right. "you injured your left leg which one still hurts?"
But, this has always been a secret advantage in mathematics since seeing patterns backwards happens as fast as forwards.
I don't mind doing measurements but here is another shot at avoiding it:
An isosceles triangle is a pendulum. The distances are the same because it's the same string. If a pendulum could swing all the way around it would make a circle.
I think focusing on the results might help? If they go top/bottom the text will be upside down.
So "flip it so the edge with the text is *still* near you but the lighter side of the board is on top" maybe?
The "left right" makes me think of rotating since with 90 degree turns left and right matter?
@dahukanna @Bumblefish @3TomatoesShort @EverydayMoggie
That sounds like so much work to me.
If you want someone with two parts that are the same length that start at the same point they have to be on a circle. No need to measure anything.
@Bumblefish @3TomatoesShort @EverydayMoggie
OK pizza good to know.
Anyway. Connecting the center of a circle to two points like that is a great way to create an angle. When you copy an angle you are just cutting two pizza slices that are the same.
If the pizzas are the same size, and the distance between the points on the circle is the same. The angle at the top (center) is the same.
@Bumblefish @3TomatoesShort @EverydayMoggie
EXACTLY!
The legs of the compass are the same length (roughly) so it makes an isosceles triangle.
@Bumblefish @3TomatoesShort @EverydayMoggie
OK now I'm confused what you have done. This is what I was expecting. But, people always surprise me.
@Bumblefish @3TomatoesShort @EverydayMoggie
Great use the center and the circle to make a pointy triangle.
@Bumblefish @3TomatoesShort @EverydayMoggie
Ok but try.
@Bumblefish @3TomatoesShort @EverydayMoggie
OK let me try this one:
How would you use a compass to make a very pointy isosceles triangle like a wizard's hat? For a quilt or something.
If anyone has ideas to make the idea of copying an angle more obvious I would love it.
I've tried pointing out that it's basically copying a triangle too. You are duplicating the length of all three sides and thus you get the angle for free.
It's "Side Angle Side" ... but that seems maybe more confusing than just doing it a few times and feeling how well it works.