Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 91Similar Triangles, Altitude, Parallel. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
Triangles BDE,GFE & GMC are each similar to triangle ABC; hence their altitudes are proportional to their corresponding sides. In other words, h1/h = BE/BC, h2/h = EG/BC & h3/h = GC/BC. Thus, h1/h + h2/h + h3/h = (BE+EG+GC)/BC = BC/BC = 1 or h = h1 + h2 + h3Vihaan: email@example.com