 If two polygons are similar, they can be divided into the same number of triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed,...  Solid Geometry - Page 394by George C. Shutts - 1913Full view - About this book
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...perimeters have the 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... | |
 | John Macnie - Geometry - 1895 - 386 pages
...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. A, U, Given: In polygons P and P', triangles A ED, ADC, ACB, similar to triangles A'E'D', A'D'C', A'C'B',... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...homologous sides. S1MILAK FIG USES PROPOSITION XIX 105 Theorem. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. EDS Appl. Prove M sim. N, etc., in given sim © Dem. B = 2 [in sim. ©] AB = BC 1H ~ 23 M and N sim.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...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 of... | |
 | Joe Garner Estill - 1896 - 214 pages
...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 AND FIFTEEN... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...QED EXERCISE. PROPOSITION XXVII. THEOREM. 272. CONVERSELY—Two si?nilar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. Given — ABCDE and FGHKL two similar polygons. To Prove— A-IBC similar to &FGH, &ACD to &FHK, and... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...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 the... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...manner, AB BC CD DE EA A'B' B'C CD' D'E' E'A' QED 225. COB. Conversely, two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. PROPOSITION XVI. THEOREM. 226. The perimeters of two similar polygons have the name ratio as any two... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...proportional. PROP. XXI. THEOREM. 267. (Converse of Prop. XX.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. 4 Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B', and E'C'.... | |
 | Mathematics - 1898 - 228 pages
...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 of the... | |
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