 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...side is to its corresponding segment. 147. Theorem II. (Converse of Theorem I.) If a line divides tioo 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 aide is to one of... | |
 | Connecticut. Board of Finance and Control - Budget - 1914 - 804 pages
...Through three points not in a straight line, but one circle can be passed (To be proved) 5 If a straight line divides two sides of a triangle proportionally it is parallel to the third side (To be proved) 6 The areas of two similar triangles are to each as the squares of any two homologous... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...AB = BD, BS = DF, ST = FH (124). Hence AC:BD=CE:DF=EG: FH (Ax. 6). QED PROPOSITION XVI. THEOREM 296. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Given: A ABC; line DE; the proportion AB : AC = AD : AE. To Prove : DE is II to BC. B Proof : Through... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...into segments which are proportional to the adjacent sides. Thenff=it Why? 395. THEOREM. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. A FH / BC FIG. 180. Given the A ABC with DE drawn so that — = . AB AC To prove that DE || BC. Proof.... | |
 | Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...DF= 20 in., GE = 18 in., CF= 5 in., BE = 2 in. Find AD, AC, BC and GC. PROPOSITION VI. THEOREM 298. If a line divides two sides of a triangle proportionally, it is parallel to the third side. To prove that DE II AB. Proof. 1. If DE is not II AB, let the parallel to AB through D meet BC in F.... | |
 | William Betz - Geometry - 1916 - 536 pages
...construct the sides of a polygon similar to the given polygon, with AG as a side homologous to m. 378. If a line divides two sides of a triangle proportionally, it is parallel to the third side. B Given the triangle ABC, and the line DE drawn so that AD AE DB ~ EC To prove that DE II BC. Proof.... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...it divides the other two sides proportionally. The converse of this theorem is: 214. Theorem XI. // a line divides two sides of a triangle proportionally, it is parallel to the third side. Given the triangle ABC with the line MN cutting the side AP AQ ABaiP and side CA at Q, forming the... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...it divides the other two sides proportionally. The converse of this theorem is: 214. Theorem XI. // a line divides two sides of a triangle proportionally, it is parallel to the third side. Given the triangle ABC with the line MN cutting the side AP AO AB at P and side CA atQ, forming the... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...ABC and meets AC at D and BC at E, then AC^BC , AC=BC AD BE DO EC. 124. Theorem. — If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Hypothesis. In A ABC, DE meets AC at D and BC at E, , ,, . DC EC such that— = — Conclusion. DE... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...point, C, so that AB :AC=: m : n, •en ro and n are two given lines. 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,... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
