 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 - 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... | |
 | 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... | |
 | 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 =... | |
 | 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,... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 344 pages
...segments on the other side. COR. If a line is parallel to the base of a triangle, one side is to either of its segments as the other side is to its corresponding segment. Suggestion. Use Th. 96. Ex. 1. In Fig. 289 prove that CD = DA CA_DA CA _C_D CE BE' CB~EB' CB~CE Ex.... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...segments on the other side. COR. If a line is parallel to the base of a triangle, one side is to either of its segments as the other side is to its corresponding segment. THEOREM 100. If a line divides the sides of a triangle so that one side is to one segment as a second... | |
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