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
| George Clinton Shutts - 1905 - 260 pages
...Complete the demonstration. OD PROPOSITION XXIII. 309. Theorem. CONVERSE OF PROPOSITION XXII. Two similar **polygons can be divided into the same number of triangles, similar each to each and similarly placed.** GA G' A' Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be drawn... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...find the shortest side of the less. 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';... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...triangles, similarly placed. Const. Therefore the polygons are similar. "If two polygons are composed of **the same number of triangles, similar each to each, and similarly placed,** the polygons are similar." § 362 MISCELLANEOUS EXERCISES PEOBLEMS OF CONSTRUCTION 777 To divide one... | |
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...A'B' QED PLANE GEOMETRY — BOOK III PROPOSITION XXIV. THEOREM 362 If two polygons are . composed of **the same number of triangles, similar each to each, and similarly placed,** the polygons are similar. HYPOTHESIS. The & ABC, ACD, and ADE are similar respectively to the A A'B'C',... | |
| 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
...each to each and similarly placed. Given : ABCDEF and GHIJKL, 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
...externally into segments proportional to the sides of the angle. 355. If two polygons are composed of **the same number of triangles, similar each to each and similarly placed,** the polygons are similar. 356. If two polygons are similar, they can be separated into the same number... | |
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