 | Arthur Schultze, Frank Louis Sevenoak - 1913 - 484 σελίδες
...807. In a given line, AB, to find a point, C, so that 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: DM. To prove DB parallel to EC. Proof. Through C, draw CE' parallel to... | |
 | Jacob William Albert Young - 1924 - 484 σελίδες
...a triangle parallel to the third side it divides these sides proportionally. (b) If a line divides two sides of a triangle proportionally it is parallel to the third side. (Proofs for commensurable cases only.) (c) The segments cut off on two transversals by a series of... | |
 | Baltimore (Md.). Department of Education - 1924 - 182 σελίδες
...it divides those sides proportionally. Proof for the commensurable case only. b. If a line divides two sides of a triangle proportionally, it is parallel to the third side. c. The segments cut off on two transversals by a series of parallels are proportional. d. The bisector... | |
 | Julius J. H. Hayn - 1925 - 328 σελίδες
...L, PARALLEL FROM PROPORTIONAL SEGMENTS 195 Proposition XII. Theorem 202. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Hyp.: Given the triangle ABC with EF so placed that CE : EA = CF : FB. Det. : To prove that EF is parallel... | |
 | National Committee on Mathematical Requirements - 1927 - 208 σελίδες
...triangle parallel to the third side it divides these sides proportionally. [57, cd] (b) If a line divides two sides of a triangle proportionally it is parallel to the third side. (Proofs for commensurable cases only.) [58*, cd*] (c) The segments cut off on two transversals by a... | |
 | Military Academy, West Point - 1934 - 964 σελίδες
...polygon whose vertices are А, В, С, D,E. В X С X XX AE D X Г 10 Theorem: If n straight line divides two sides of a triangle proportionally, it is parallel to the third side. I 10 Problem: Inscribe a regular decagon In a given circle. I 10 Theorem: ADCD is »given square. E,... | |
 | Research & Education Association Editors, Ernest Woodward - 2012 - 1080 σελίδες
...line parallel to one side of a triangle divides the other two sides proportionally. If a line divides two sides of a triangle proportionally, it is parallel to the third side. The bisector of one angle of a triangle divides the opposite side in the same ratio as the other two... | |
 | The Editors of REA - 2013 - 112 σελίδες
...A /\ If DE II BC, then / \ AD-AE D / _ \ F BD ~ CE ~/ NT Figure 8.1 e C Theorem 2 If a line divides two sides of a triangle proportionally, it is parallel to the third side. Theorem 3 The bisector of one angle of a triangle divides the opposite side in the same ratio as the... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 356 σελίδες
...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 —- A— G B Given the triangle ABC, and the line DE drawn so that AD AE &B~1$C' To prove that DE... | |
 | 646 σελίδες
...Statements (1), (2) and (3). 1. (ii) Converse of the Basic Proportionality Theorem If a straight line cuts two sides of a triangle proportionally, it is parallel to the third side. A B C AP AQ Given : A straight lien PQ cuts AB and AC {produced in (ii)} in the same ratio ie ——... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
