| 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 - 320 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 - 320 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 - 392 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, Plane - 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 - 1899 - 400 pages
...Bid : B 2 C 2 = = r. .'. A^ + JBiCi + :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 Of coincide, and the figures can be placed having 0 within each. The triangles AiOB... | |
| |