Transformation Dance Studio

Every move on this dance floor is a transformation. Slides, flips, and spins keep the dancer exactly the same size — congruent. One move changes everything: the dilation. Learn the choreography, then read any move from its coordinates alone.

Grade 8 · Unit 5 8.G.1 Properties of rigid motions 8.G.2 Congruence 8.G.3 Coordinate rules 8.G.4 Similarity 8.G.5 Angle facts

Part 1

The Dance Floor

Your dancer is triangle ABC; the dashed gold ghost never moves — it's the original. Try every move and watch the coordinate rule appear. The verdict below tracks the big question: is the dancer still congruent to the ghost, or merely similar?

Dancer's coordinates

Part 2

Name That Move

The studio's security camera caught only the before-and-after coordinates. Lock in your prediction first — which move was it? Then the reveal tests every suspect against every point.

Case 1 of 5

Part 3

The Studio Machines

Three machines backstage: apply any coordinate rule step by step, prove congruence or similarity with a sequence of moves, and settle every angle question a triangle can ask.

Every move has a coordinate rule. Feed triangle (1, 1), (4, 1), (1, 3) through each one.

Pick a rule:

Congruent means a sequence of rigid moves lands one shape exactly on the other. Add one dilation and the verdict changes to similar.

Pick a proof:

Triangle angle sum, exterior angles, and parallel lines cut by a transversal — the three angle facts of 8.G.5, each proven and then used.

Pick a job:

Part 4

Recital Quiz

Ten questions to earn your place in the company. Wrong answers get a hint naming the exact machine or dance move that proves the right idea.

📦 Word Box

Transformation: A move that takes every point of a figure to a new position — a dance step for shapes.
Translation (slide): Every point moves the same distance in the same direction: (x, y) → (x + a, y + b).
Reflection (flip): A mirror image across a line: over the x-axis, (x, y) → (x, −y); over the y-axis, (x, y) → (−x, y).
Rotation (spin): A turn about a fixed point: 90° counterclockwise about the origin is (x, y) → (−y, x).
Dilation: A resize from a center point: (x, y) → (kx, ky). The only move here that changes size.
Rigid motion: A transformation that preserves all lengths and angles: translations, reflections, and rotations.
Congruent (≅): Identical in shape AND size — one figure lands exactly on the other after a sequence of rigid motions.
Similar (~): Same shape, possibly different size — reachable by rigid motions plus a dilation. Equal angles, proportional sides.
Scale factor (k): The dilation's multiplier: every length ×k. k > 1 enlarges; 0 < k < 1 shrinks.
Coordinate rule: The algebra of a move: what happens to (x, y). Every transformation has one.
Transversal: A line crossing two parallel lines, creating matching angle pairs.
Alternate interior angles: Angles on opposite sides of a transversal, between the parallels — always equal.
Exterior angle: The angle between one side of a triangle and the extension of another — equal to the sum of the two remote interior angles.