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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