If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Plane Geometry - Page 170by Webster Wells, Walter Wilson Hart - 1915 - 309 pagesFull view - About this book
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...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 same number... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...is, the 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... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...is, the 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 0 within each, and the triangles A1OB1, 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
...like 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... | |
| |