Geometry, Lesson 2
Move It, Keep Its Structure
A transformation changes where a figure is. Geometry asks what the motion cannot change.
Predict, then translate, rotate, and reflect the same triangle.
Look for properties inside the figure, not its place on the screen.
Choose before the moving image appears.
Find the rigid invariants
Answer all five before congruence is explained through transformations.
Compose motions
Order changes the destination
Begin at (2, 1). Compare translating 2 units right before a quarter-turn with doing the same moves in reverse order.
Play the two-step journey and watch the intermediate point.
Think in ordered actions
Complete all five before comparing the two transformation chains.
Symmetry
A motion that leaves the whole unchanged
Choose a shape and a possible mirror line. Reflect it and judge exact overlap.
Recognise symmetry as invariance
Answer all five before each possible axis is explained.
The geometric question
Next: let small changes build a whole.
Analysis connects a changing rate to the total it accumulates.