 If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',...  Elements of Geometry and Trigonometry: With Notes - Page 73by Adrien Marie Legendre - 1828 - 316 pagesFull view - About this book
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...the lengths of D'E' and E'C'. BOOK III.— SIMILAR FIGURES. Proposition 2 1 . Theorem. 320. If two polygons are composed of the same number of triangles similar each to each, and similarly placed, the polygons are similar. Hyp. Let the AS ABC, ACD, ADE of the polygon ABCDE be similar respectively... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...polygons may be divided into the same number of similar triangles, similarly placed. PROP. XIII. Polygons composed of the same number of triangles, similar each to each, and similarly placed, are similar. PROP. XIV. The perimeters of similar polygons are proportional to any homologous... | |
 | William Chauvenet - 1893 - 340 pages
...PROPOSITION V. Two triangles are similar when their homologous sides are proportional. PROPOSITION VI. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...draw a line parallel to one' of the given lines (Art. 226.) PROPOSITION XIX. THEOREM. * 236. // two polygons are com,posed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Let the polygons AB CD EF and A' B' C' D E' F be composed of the... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...and similarly placed, the polygons are similar. Let the polygons AB CD EF and A' B' C' D' E' F' be composed of the same number of triangles, similar each to each and similarly placed, ABC being similar to A' B' C ', and so on for the other triangles. To prove that the polygons... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...Theorem. The homologous bases of similar triangles are to each other as their altitudes. 227. Theorem. Two similar polygons are composed of the same number of triangles, similar pair by pair, and similarly placed. 228. Theorem. Two polygons are similar if they are composed of... | |
 | John Macnie - Geometry - 1895 - 390 pages
...those mutually parallel or perpendicular. PROPOSITION XVII. THEOREM. 294. Two polygons are similar if composed of the same number of triangles similar each to each and similarly placed. D ~4' Given: In polygons p and P', triangles AED, ADC, ACB, similar to triangles A'E'D', A'D'C',... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...lines intercept proportional segments upon two parallels, they pass through a common point. 331. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 332. If two polygons are similar, they are composed of the same number... | |
 | Joe Garner Estill - 1896 - 214 pages
...Show how to inscribe in a given circle a regular polygon similar to a given regular polygon. 6. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. The University of Chicago, September, 1896. TIME ALLOWED, ONE HOUR... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...AC = 36, what is the length of EC? Puoros1T1oN XVIII 210. Theorem. Two polygons are similar if they are composed of the same number of triangles similar each to each and similarly placed. Appl. Dem. Msim.N Psim. Q Rs'im.S Prove © sim. x = z Y = V C=3 AC^BC .LO & O 14} & G [in sim.... | |
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