M29 · Overview Transformations and congruence mind map

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M29 · Overview Transformations and congruence mind map

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Rigid moves

Translate: Same vector every vertex; components signed displacement
Reflect: Name mirror line; equal perpendicular distances; axis rules
Rotate: Centre, angle, direction; 90° anticlockwise: (a,b)→(−b,a)

Enlarge

Centre / factor: Scale centre-to-vertex vectors; relative positions, not origin
Size: 0<k<1 reduces; angles stay; rigid moves preserve lengths

Congruence

Tests: SSS, SAS, ASA/AAS, RHS; SAS angle must be included
Proof: Match vertices in order, name test, deduce equal parts

Further moves

Negative: Higher: Opposite side of centre; −2 doubles distance, reverses vector
Order: Higher: Apply in stated order; translations add vectors
Reflections: Higher: Parallel mirrors → translation; intersecting → rotation

Connections

Rigid moves → Congruence: Rigid moves preserve congruence
Enlarge → Further moves: Enlargement scales vectors relative to its centre