 | John Macnie - 1895 - 390 σελίδες
...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', A'C'B',... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - 346 σελίδες
...ratio r, which is the ratio of the corresponding sides. 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and 0' coincide, the figures can be placed having O within each, and the triangles AiOBi, A2OB2... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - 344 σελίδες
...ratio r, which is the ratio of the corresponding sides. 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and 0' coincide, the figures can be placed having 0 within each, and the triangles A1OB1, A2OB2... | |
 | Joe Garner Estill - 1896 - 214 σελίδες
...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,...each, and similarly placed, the polygons are similar. The University of Chicago, September, 1896. TIME ALLOWED, ONE HOUR AND FIFTEEN MINUTES. [When required,... | |
 | George D. Pettee - 1896 - 272 σελίδες
...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. & M... | |
 | George Albert Wentworth - 1896 - 68 σελίδες
...each to each, and similarly placed, the polygons are similar. 332. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. 333. The perimeters of two similar polygons have the same ratio as any two homologous sides. 334. If... | |
 | Henry W. Keigwin - 1897 - 254 σελίδες
...C, /_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...each and similarly placed, the polygons are similar. 272. THEOREM. If two polygons are similar, they may be resolved into the same number of triangles,... | |
 | George Washington Hull - 1897 - 408 σελίδες
...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 to LG. Dem.—Since... | |
 | Webster Wells - 1898 - 250 σελίδες
...homologous base of a similar triangle is PROI-. XX. THEOREM. 266. Tiro polygons are similar irhen the;/ are composed of the same number of triangles, similar each to each, and similarly placed. Given, in polygons AC and A'C", A ABE similar to A A'B'E', A BCE to AB'C'E', and A CDE to A GD'E'.... | |
 | James Howard Gore - 1898 - 232 σελίδες
...of their sides is a parallelogram. PROPOSITION XV. THEOREM. 224. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. A Let ABCDE and A'B'C'D'E' be two polygons composed of the same number of similar triangles similarly... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
