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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 - 486 pages
...internally; 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 side is to its corresponding segment. For AD:DB = AE: EC. By composition AD + DB:DB = AE + EC:EC, or AB:DB = AC: EC. 296. COR. 2. Three parallel...

Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...? Therefore, DE II AB. 148. Corollary 1. If a line cuts two sides of a triangle in such a way that either side is to one of its segments as the other side is to its corresponding segment, then the line is parallel to the third side 149. Theorem III. Tlie bisector of an angle of a triangle...

Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...be proved, CD /DA = CE/EB. 146. Corollary 1. If a line is drawn parallel to the base of a triangle, either side is to one of its segments as the other side is to its corresponding segment. Given the A ABC and DE II AB. (See Fig. 107.) To prove (1) that CA/CD = CB/CE and (2) that CA/DA =...

Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...other sides proportionally. 146. Corollary 1. If a line is drawn parallel to the base of a triangle, either side is to one of its segments as the other side is to its corresponding segment. 147. Theorem II. (Converse of Theorem I.) If a line divides tioo sides of a triangle proportionally,...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...either side is to one of its segments as the other side is to its corresponding segment. For AD:DB = AE: EC. By composition AD + DB : DB = AE + EC: EC, or AB : DB = AC: EC. 296. COR. 2. Three parallel A i \ D lines cut off proportional segments ' ~~~' ^ on any two transversals....

Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...! Therefore, DE II AB. 148. Corollary 1. If a line cuts two sides of a triangle in such a way that either side is to one of its segments as the other side is to its cot-responding segment, then the line is parallel to the third side 149. Theorem III. Tlie bisector...

Robbin's New Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...midpoint of arc BC, meeting chord CB at D. The triangles ABD and ACP are PROPOSITION XXI. THEOREM 305. If a line parallel to one side of a triangle intersects the other sides, the triangle formed is similar to the original triangle. Given : MN II to BC in A ABC. To Prove...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 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...+ DB : DB = AE + EC : EC, or AB : DB — AC : EC. 296. COR. 2. Three parallel lines cut off proportional segments on any two transversals. HINT. Draw...