Archimedes Laboratory Project™
Puzzles & Mental Activities that Enhance Critical and Creative Thinking Skills

ABC is an equilateral triangle. P is an arbitrary point where segments a, b and c meet. Segment c is perpendicular to AB. Segment a is perpendicular to BC. Segment b is perpendicular to AC. Prove that a + b + c = h (height of the triangle)
ABC est un triangle équilatéral. P est un point quelconque où les segments a, b et c se rencontrent. Segment c est perpendiculaire à AB. Segment une est perpendiculaire à BC. Segment b est perpendiculaire à AC. Montrer que a + b + c = h (hauteur du triangle)
ABC è un triangolo equilatero. P è un punto arbitrario dove i segmenti a, b, e c si incontrano. Segmento c è perpendicolare ad AB. Segmento a è perpendicolare a BC. Segmento B è perpendicolare ad AC. Dimostrare che a + b + c = h (altezza del triangolo).

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Solution: As triangle ABC is equilateral: AC = BC = AB = x Then hx/2 = ax/2 + bx/2 + cx/2 Simplifying hx = x(a + b + c) Thus h = a + b + c QED See also the neat visual proof below: Please spread the word about the Sunday Puzzle!