This is an idea for working with parallel, perpendicular and intersecting lines to get at types of angles and their relationships.

I'm imagining that students are familiar with the words parallel, perpendicular, intersecting, right, acute, obtuse, complementary and supplementary (as most high schoolers are). The idea for the question cards comes from a video of a japanese classroom where there were hint cards at the front of the room that students could go look at when they were stuck.

Big question on board:
What can you make with two lines?
*remember, lines continue forever

Answers I’m hoping for: (note: I'm not expecting students to use this vocabulary from the start, but I'll push for precision whenever possible, especially at the end when we make a final list)
4 right angles (perpendicular)
2 obtuse and 2 acute angles
supplementary angles (always)
complementary angles (sometimes)
no angles (parallel)
all add up to 360
opposite angles congruent

Extra questions on cards: (for me to randomly drop on desks, and sitting at the front with a sign: think you have them all? check if you’ve answered these questions)
What is the maximum and minimum number of angles you can make?
What size angles can you make?
What do the angles add up to?

Big question on board:
What can you make with three lines?

Answers I’m hoping for:
max 12 angles, min 0 angles
also options: 8 and 6
perpendicular: 8 right angles
parallel + transversal only has 2 angles (congruent or supplementary)
all angles at one intersection sum to 360
different total sums for different numbers of intersections
angles next to each other still supplementary
angles opposite each other still equal
a triangle, with things pointing out of it

Extra questions on cards: (for me to randomly drop on desks, and sitting at the front with a sign: think you have them all? check if you’ve answered these questions)
What is the maximum and minimum number of angles you can make?
What size angles can you make?
What do the angles add up to?
What kinds of lines make ‘nice’ angles? (lots of patterns)

After a long time of pushing students to work individually, then share with neighbors, to the point that they are all quite confident they have all the possibilities and can explain why there aren't any other options:
Share out all conjectures
Prove any we can, offer any counterexamples we have
Type up the list and assign/define vocab words as needed
separate list into: confident of truth and open question

Open questions I'd like to see: what happens with more lines? what if the lines weren't coplanar?
Who knows what else, that's actually what I'm really excited about- hearing their questions!

Goals: vertical angles, linear pairs, angle sum rule, full rotation=360, pattern of parallel lines and a transversal.

My question: when do we introduce vocabulary and how much? If this is the first study of angles it will be vocab overload. Maybe just name vertical angles and linear pairs since they'll come up over and over in this exploration. Alternate interior and all that nonsense will just have to wait (although using the words interior and exterior, consecutive and alternate in passing isn't a terrible idea since they should all be familiar)