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If a line parallel to one side of a triangle intersects the other two sides, either side is to one of its segments as the other side is to its corresponding segment. For AD:DB = AE : EC.
Plane and Solid Geometry - Page 123
by Arthur Schultze - 1901

## Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...; if it meets their prolongations, the sides are divided externally in the same ratio. 295. COR. 1 If a line parallel to one side of a triangle intersects...the other two sides, either side is to one of its seg ments as the other side is to its corresponding segment. For AD : DB = AE : EC. By composition...

## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1925 - 504 pages
...if it meets their prolongations, the sides are divided externally in the same ratio. 294. COR. I. // a line parallel to one side of a triangle intersects...as the other side is to its corresponding segment. Proof: Using figure for the proposition, we can show that AB = (m + n)(AF) and AD = m(AF). Hence AB...

## Geometry I Essentials

The Editors of REA - Mathematics - 2013 - 112 pages
...similar triangles have the same ratio as the measures of any pair of corresponding sides. Corollary 3 If a line parallel to one side of a triangle intersects the other two sides, then it cuts off a triangle similar to the original triangle. Corollary 4 Two triangles which are similar...