Real-World Problem Solving with Similarity
Using shadows and light sources to measure heights indirectly. When parallel rays create similar triangles, we can find unknown heights using proportional relationships.
When triangles are similar, their medians are also proportional. This extends similarity beyond just sides and angles to internal segments and special lines.
Measuring impossible distances and heights using similar triangles. From ancient Greek calculations of Earth's circumference to modern surveying techniques.
Architecture, engineering, map-making, and navigation all rely on similar triangle principles. Scale factors and proportional relationships are everywhere in design and construction.