Welcome to a geometry adventure — angles, triangles, and prisms. You won't just memorise rules here — you'll build them yourself with drawings, discussions, and a healthy dose of "what if…?"
Every task here asks you to notice, wonder, and argue (nicely!) about what's true. Work with a partner or a small random group whenever you can — talking is how your brain makes sense of new ideas. If you're stuck, that's a sign your brain is learning something new. Don't rush to the answer; rush to the question behind the question.
There's no secret "maths gene" — only the work you've put in so far, and the work still ahead.Each module starts with a puzzle, not a definition. Start anywhere that sparks your curiosity — or follow the sequence below.
When do three side lengths actually form a triangle? What makes a shape unique — and what makes it wobble?
Right angles, straight angles, pairs that play together, and equations that unlock unknown angles.
Slicing solids, measuring volume, wrapping surfaces. Geometry that lifts off the page.
Real situations. Messy numbers. Everything you've learned so far — now working together.
This module unfolds across four lessons. Pick one to begin — or move through them in order. Each one builds on the last, but every lesson starts with a puzzle you can reason through on your own.
If you can turn all the way around (360°), what happens if you turn halfway? A quarter of the way? And what do those turns have to do with the corner of a square or the point of a hexagon?
You'll be able to recognise 90°, 180°, and 360° angles, use pattern-block reasoning to figure out any regular polygon's interior angle, and find unknown angles by combining the ones you know.
When two angles share a vertex and a side without overlapping, we call them adjacent angles. Adjacent angles can be combined — they "add up" along the rays they share.
Stack regular polygons around a single point. Watch the total turn. Which combinations fit perfectly? What does "perfectly" tell you about the corner angles?
Two angles are sitting next to each other. If you know one, can you figure out the other? The answer is "only if you know how they're related." Let's find out the two most useful relationships.
Getting stuck is not the opposite of learning — it's part of it. If your first idea doesn't work, that's not failure; it's learning. Try a different drawing, measure something, or debate with a partner.
Drag the ray to split a right angle into two parts. The two parts are complementary — their measures add to 90°, no matter how you split it.
Drag the ray to split a straight angle. The two parts are supplementary — their measures always sum to 180°.
Adjacent complementary/supplementary angles sit side-by-side. But angles don't have to be adjacent to be complementary or supplementary — the relationship is about their measures, not their positions.
Each tap cycles: complementary → supplementary → neither → unsorted.
When two straight lines cross, four angles appear. They come in two pairs with a secret relationship — one that holds no matter how the lines cross. Your mission: find the pattern and prove why it's always true.
This topic begs for a vertical non-permanent surface — a whiteboard, a window, a big sheet of butcher paper on the wall. Stand with your group. Draw big. Argue. Erase. Redraw.
Rotate the pink line. Watch all four angles. Which pairs are equal to each other? Which pairs add to 180°? Make a claim before reading the reveal.
Why the name "vertical"? Not because they point up — because they share the same vertex. Confusing, but true. Blame the Romans.
Now that you know how angles relate, you can write equations that capture those relationships. Algebra isn't a new monster — it's just a shorter way of saying what you already know.
"Because these angles are ______, I know their measures add to ______. So I can write ______ = ______. Solving gives x = ______."
Use this stem every time you set up an equation today.
Since these angles are vertical, they must be equal. Set the expressions equal to each other:
Pick one task from today that challenged you most. Tell a classmate:
Unanswered questions are gold. Hang onto them.
If I give you three side lengths, can you always build a triangle? Sometimes the answer is yes, sometimes no, and sometimes there's more than one way. Your mission: figure out which is which, and why.
You'll know when three measurements force a unique triangle, when they allow many triangles, and when they make no triangle at all. You'll also handle quadrilaterals and other polygons.
Given any three sides, a triangle exists only if:
Why? If the longest side were longer than or equal to the sum of the other two, the two shorter sides couldn't stretch far enough to meet.
Tap cycles: makes a triangle → impossible → unsorted.
AAA (three angles) gives you infinite similar triangles of different sizes. SSA sometimes gives you two different triangles.
If you slice through a 3D shape, what shape does the cut reveal? How much space does a 3D object take up — and how much "skin" wraps around it? Welcome to thinking in three dimensions.
3D is hard to see on paper. Use your hands. Grab a cereal box, a soup can, a Toblerone bar. Turn them, slice them mentally, trace the faces with your finger. Geometry is physical before it's abstract.
The real test of understanding isn't remembering a formula — it's knowing which formula to pull out when a messy, real-world problem lands on your desk. Module IV brings together everything you've learned.
"I don't know" is a fine starting place. "I don't know yet" is better. These problems have many entry points — pick one and start sketching. Don't wait for the "right" method to appear.
Pick one task from this entire unit that challenged you most. Tell a classmate:
Unanswered questions are gold. Hang onto them.