M26 Similarity and proportional measures mind map

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M26 Similarity and proportional measures mind map

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Similar / congruent

Correspondence: Similar: same angles, proportional sides; congruent: k=1
Triangles: AA proves similarity; not congruence; trig ratios unchanged

Lengths

Factor: Large/small matching lengths; reverse uses reciprocal
Perimeter: Every length ×k → perimeter ×k

Area / volume

Powers: Higher: Length k → area k² → volume k³
Reverse: Higher: Square root area factor; cube root volume factor

Applications

Material: Higher: Same density: mass follows volume; paint follows area
Condition: Higher: Establish similarity; changing one dimension is insufficient

Connections

Similar / congruent → Lengths: Matching sides determine one length factor
Area / volume → Applications: Dimensions determine square or cube scaling