 | 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.... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
.../_K—£D, etc., and the homologous sides are in the ratio of similtude AB : HI. 271. THEOREM. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. 272. THEOREM. If two polygons are similar, they may be resolved into... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...DF* =CM*iFN* = AM1 : DN*. § 128 PROPOSITION XXVI. THEOREM. 271. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Given—A .4-BC similar to AFC ' //, A^CD to &FHK, and &ADE to &FKL. To Prove—EB similar... | |
 | Yale University - 1898 - 212 pages
...center, the nearer is the greater. 3. Define similar polygons, similar sectors, similar segments. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 4. The areas of similar segments have the same ratio as the squares... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
