...; 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...

...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...

...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...

...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,...

...corresponding sides. AreaofA^g£_ 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...