 | Alan Sanders - Geometry - 1908 - 396 pages
...in this proposition. and PROPOSITION XIV. THEOREM (CONVERSE OP PROP. XIII.) 474. If a line divides two sides of a triangle proportionally, it is parallel to the third side. A B' . AD AE - = - . DB EC To Prove DE parallel to BC. Proof. Suppose DE is not parallel to BC and that... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...the base of a triangle divides the other two sides proportionally. 341. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. 344. Mutually equiangular triangles are similar. 347. Triangles that have an angle in each equal, and... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...across the upright piece; across the horizontal piece. PROPOSITION X. THEOREM 276. If a line divides two sides of a triangle proportionally, it is parallel to the third side. BO Given the triangle ABC with EF drawn so that EB _ FC ~AE~~AF' To prove that EF is II to BC. Proof.... | |
 | Geometry, Plane - 1911 - 192 pages
...angle formed by a tangent and a chord is measured by one-half the intercepted arc. 3. Demonstrate: If a straight line divide two sides of a triangle proportionally, it is parallel to the third side. 4. Construct: A parallelogram equivalent to a given square, and having the difference of its base and... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...the given polygon, with AG as a side homologous to m. PROPOSITION IV. THEOREM 378. If a line divides two sides of a triangle proportionally, it is parallel to the third side. A Given the triangle ABC, and the line DE drawn so that AD AE DB~1SC To prove that DE II BC. Proof. 1.... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...the given polygon, with AG as a side homologous to m. PROPOSITION IV. THEOREM 378. If a line divides two sides of a triangle proportionally, it is parallel to the third side. A c Given the triangle ABC, and the line DE drawn so that AD _ AE ZM? ~ £C To prove that DE II BC. Proof.... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...= b:c; (6) x = ^' PROPOSITION XIII. THEOEBM (Converse of Prop. XI) 415, If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. B D/ AFEC Given A ABC, and DE so drawn that — = — . AD AE To prove DE II BC. ARGUMENT 1. DE and... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...proportions can you write down for Ex. 6 ? 147. Theorem II. ( Converse of Theorem /.) If a line divides two sides of a triangle proportionally, it is parallel to the third side. c FIG. 109 Given the A ABC and the line DE dividing the sides proportionally ; that is, such that CD/... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...In a given line, AB, to find a point, C, so that AI PROPOSITION XVI. THEOREM 300. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Given in A AEC, AB:BC=AD: DE. To prove DB parallel to EC. Proof. Through C, draw CE' parallel to BD,... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...other side is to its corresponding segment. 147. Theorem II. (Converse of Theorem I.) If a line divides two sides of a triangle proportionally, it is parallel to the third side. 148. Corollary 1. If a line cuts two sides of a triangle in such a way that either side is to one of... | |
| |
If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
