Three fences of a triangular garden meet pairwise at the three corner posts and
MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Euclid's Geometry · Introduction to Euclid's Geometry
Problem
Three fences of a triangular garden meet pairwise at the three corner posts A,B and C. A gardener insists that two of these fences, say AB and AC, also meet at an interior point D inside the garden.
(a) Explain why the gardener’s statement leads to a contradiction with Euclid’s theorem on common points of two lines.
(b) Give a logically complete proof that no interior point like D can exist which lies simultaneously on extensions of both fences AB and AC if AB and AC are regarded as straight lines.