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 123by Arthur Schultze - 1901Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| Alfred S. Posamentier - Mathematics - 2002 - 276 pages
...third side of the triangle. III. Similarity A. When a line is parallel to one side of a triangle 1 . **If a line parallel to one side of a triangle intersects the other two sides,** then it divides these two sides proportionally. 2. If a line divides two sides of a triangle proportionally,... | |
| Thomas Hyun - Mathematics - 2006 - 486 pages
...corresponding sides. AreaofA^gŁ_ AE2 _ 192 = 361 Area of ADFE ~ DE2 ~ I2 ~ 49 1 7-7. Proportional Parts **If a line parallel to one side of a triangle intersects the other two sides,** then it divides those sides proportionally. In MBC , if AC \\ DE then it follows that BD__BE DA EC... | |
| |