 | George Clinton Shutts - Geometry - 1894 - 412 pages
...demonstration. PROPOSITION XXIII. 309. Theorem. CONVERSE or PROPOSITION XXII. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. GA Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be... | |
 | 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,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 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 O within each, and the triangles AiOBi,... | |
 | John Macnie - Geometry - 1895 - 390 pages
...A'B' = BC : B'C' = AC : A'C' = CD : C'D', etc. ; 149 PROPOSITION XVIII. THEOREM. 295. Conversely, two similar polygons may be divided into the same number of triangles, similar to each other and similarly placed. Given: ABCDE, or P, and A'B'C'D'E', or P', two similar polygons;... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...homologous sides. S1MILAK FIG USES PROPOSITION XIX 105 Theorem. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. EDS Appl. Prove M sim. N, etc., in given sim © Dem. B = 2 [in sim. ©] AB = BC 1H ~ 23 M and... | |
 | 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... | |
 | 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...of triangles, similar each to each, and similarly placed. PROPOSITION XVI. THEOREM. 226. The perimeters of two similar polygons have the name ratio as... | |
 | 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',... | |
 | 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 two pairs... | |
 | 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,... | |
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FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
