MathDB

9.6

Part of 1993 All-Russian Olympiad Regional Round

Problems(1)

exists line \\ ta a given cutting 3 right triangles into congruent segments

Source: All - Russian Regional Olympiad (Round 4) 1993 9.6

8/26/2024
Three right-angled triangles have been placed in a halfplane determined by a line ℓ\ell, each with one leg lying on ℓ\ell. Assume that there is a line parallel to ℓ\ell cutting the triangles in three congruent segments. Show that, if each of the triangles is rotated so that its other leg lies on ℓ\ell, then there still exists a line parallel to ℓ\ell cutting them in three congruent segments.
geometryright triangle