 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,...  Solid Geometry - Page 394by George C. Shutts - 1913Full view - About this book
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...same number of triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar each to each, and similarly placed, the two polygons are similar. Proposition VII. A Problem. 212. A polygon being given, on a line corresponding... | |
 | George Albert Wentworth - 1889 - 276 pages
...homologous angles, vertices, sides, and diagonals. 154. Theorem. Two similar polygons are divisible into the same number of triangles, similar each to each, and similarly placed. 155. Theorem. Two polygons are similar if they are divisible into the same number of triangles, similar... | |
 | George Albert Wentworth - 1889 - 264 pages
...each to each, and . similarly placed. 155. Theorem. Two polygons are similar if they are divisible into the same number of triangles, similar each to each, and similarly placed. 156. Theorem. The perimeters of two similar polygons are proportional to any two homologous sides.... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...sidet proportional (307). QED Proposition 22. Theorem. 321. Conversely, two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. Hyp. Let ABCDE, A'B'C'D'E' be two similar polygons divided into As by the diagonals AC, AD, A'C', A'D'... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...and DE = 5, find B'D', D'E', and AE'. Proposition 21 . Theorem. 320. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. Hyp. Let the As ABC, ACD, ADE of the polygon ABCDE be similar respectively... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...Conclusion : AB 0 and GHJ being any similar, etc. PROPOSITION XIII. 4O4. Theorem : Polygons composed of the same number of triangles, similar each to each, and similarly placed, are similar. Statement: Let any polygons, ABK and FSI, contain the same number of triangles, /, 2,... | |
 | William Chauvenet - 1893 - 340 pages
...similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...placed, the polygons are similar. PROPOSITION XX. CONVERSE OF PROP. XIX. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. PROPOSITION XXI. The ratio of the perimeters of two similar polygons equals the ratio of similitude... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 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. 4. In the triangle whose sides are a, b, and c, determine the segments of each side made by the bisector... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...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... | |
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