 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,...  Plane and Solid Geometry, Suggestive Method - Page 376by George Clinton Shutts - 1913 - 476 pagesFull view - About this book
 | International Correspondence Schools - Building - 1906 - 634 pages
...radius? Ans. 13i in. OTHER SIMILAR POLYGONS 32. Two polygons are similar when they are composed of the same number of triangles similar each to each and similarly placed. Thus, in Fig. 25, the polygons ABCDE and A' B> C1 D> E> are composed of the same number of similar... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...side of the less. PLANE GEOMETRY 327. THEOREM. If two polygons are similar, they may be decomposed into the same number of triangles similar each to each and similarly placed. Given : Similar polygons BE and B'E'. To Prove : A ABC similar to A A'B'C'; AACD similar to A A'C'D';... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...similarly placed. IJ Given: ABCDEF and GHUKL, two similar polygons. To Prove : That the polygons can be divided into the same number of triangles, similar each to each and similarly placed. Proof : From the corresponding vertices A and G draw all diagonals possible. Then A CAB ~ A IGH. (§... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...manner, = = PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may lie decomposed into the same number of triangles, similar each to each, and similarly placed. 4 Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous ; and diagonals EB, EC,... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...like manner, PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. Z» Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous; and diagonals EB, EC,... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...(Why?) THEOREM XVII (Converse of Theorem XVI) 356. If two polygons are similar, they can be separated into the same number of triangles, similar each to each and similarly placed. Given : ABCDEF and GHIJKL, two similar polygons. To Prove : That the polygons can be divided into the... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...double the given triangle? (Two cases.) 293. Theorem VIII. // 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,... | |
 | Education - 1909 - 720 pages
...equal to one-half of the third side. 2. Demonstrate: If two polygons are similar, they may be separated into the same number of triangles, similar each to each, and similarly placed. 3. Construct a fourth proportional to three given lines. 4. Demonstrate : Of isoperimetria polygons... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 204 pages
...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, the polygons are similar. 295. Theorem X. The areas of similar polygons have the same ratio as the... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...AEF are similar. PROPOSITION XVIII. THEOREM 292. If two polygons are similar, they can be separated into the same number of triangles, similar each to each, and similarly placed. Given two similar polygons ABCDE&nA A'B'C'D'E' with angles A, B, C, D, E equal to angles A', B', C',... | |
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