 If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',...  Elements of Geometry and Trigonometry: With Notes - Page 73by Adrien Marie Legendre - 1828 - 316 pagesFull view - About this book
 | 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... | |
 | Mathematics - 1898 - 228 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... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...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... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...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... | |
 | Education - 1901 - 814 pages
...point are equal, and make equal angles with the line ; the point to the center. 3 Prove that if two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...E'C'D' are similar. §351 § 351 Ax. 1 §357 QED PROPOSITION XXVI. THEOREM. 366. CONVERSELY : If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB,... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...§351 Ax. 1 § 357 QEO BOOK III. PLANE GEOMETRY. PROPOSITION XXVI. THEOREM. 366. CONVERSELY : If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB,... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...triangle similarly situated in , Proposition 142. Theorem. 176. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Since the homologous A are either homologous A of similar A, or else the sums of such A, the... | |
| |
