Teach the Cast
Some of GeometryForge’s cast are still learning. When you teach them, YOU learn it best — catch what they get wrong, then quiz them.
Teach Master Hypotenuse
Teach the connections
Show how the geometry ideas connect
Sir Transverse (parallel-line transversals (proportional segments — the intercept theorem)) × Scout Scale (dilation & similarity)
Why does drawing a line PARALLEL to one side of a triangle create a smaller SIMILAR triangle?
Sir Transverse then says: “The small triangle's sides are the big one's MINUS a fixed amount — you subtract to shrink it.” — is that right?
Now they see it: similarity isn't a separate rule — it grows straight out of parallel-line proportions.
Master Tangent (tangent-to-a-circle & the tangent-chord angle) × Lady Inscribed-Angle (inscribed-angle circle theorems)
A tangent-chord angle and an inscribed angle both sit on the same arc. How are their sizes related?
Master Tangent then says: “The tangent-chord angle equals the WHOLE arc, since the tangent runs along the edge.” — is that right?
Now they see it: circle angles aren't a pile of separate rules — they all trace back to the arc.
Compass Wraith (locus — a circle is the set of points equidistant from a center) × Captain Construction (compass-and-straightedge constructions)
Why does swinging a compass from two points and marking the crossings give the perpendicular bisector?
Compass Wraith then says: “A construction is just careful drawing — the compass size doesn't have to match between the two arcs.” — is that right?
Now they see it: a construction isn't drawing — it's building a locus, point by equidistant point.
Capstone — design a circular garden with a triangular bed
You're designing a round garden with a triangular flower bed inside. Each part below needs ONE of the cast's ideas — bring in the right person for each.
Plot the three corners of the bed as exact points on the grid.
Find how much soil the triangular bed needs — its area.
Check the bed is a right triangle: do the two short sides satisfy a² + b² = c²?
Draw the round garden border with compass and straightedge.
Resize the whole design to fit a bigger yard, keeping the exact shape.
The whole cast, working together — because you taught each one and saw how they fit.
Your concept map