 | 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
...B'E' B'C ' BE BC In 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...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... | |
 | Yale University - 1898 - 212 pages
...escribed, and circumscribed circles of any triangle. 3. (a) Two polygons are similar when composed of the same number of triangles, similar each to each and similarly placed, (b) When the areas of two similar polygons are in the ratio of in to n, in what ratio are the homologous... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...BE, and CF meet in a point. Therefore, etc. QBD Proposition XII 309. Draw two polygons such that they may be divided into the same number of triangles, similar, each to each, and similarly situated. How do the homologous angles of these polygons compare in size ? How do the ratios of any... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...Bid : B 2 C 2 = = r. .-. AiBi + B1C1 + :A 2 B 2 + B 2 C 2 + =r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and O" coincide, and the figures can be placed having 0 within each. The triangles AiOBi, A^OB... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...Bid : B 2 C 2 = = r. .'. A^ + JBiCi + :A 2 B 2 + B 2 C 2 + = r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and Of coincide, and the figures can be placed having 0 within each. The triangles AiOB i , A... | |
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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. 
