| 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,... | |
| William James Milne - Geometry - 1899 - 398 pages
...Consequently, AD, BE, and CF meet in a point. Why? 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... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
........ = r. .•. AiBi + BiCi + ..... :A2B2 + J52C2 + ..... =r. (Why?) 4. I wo similar polygons can **be divided into the same number of triangles similar each to each, and** similarli/ placed. For O and CX coincide, and the figures can be placed having 0 within each. The triangles... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...Theorem. 175. If two polygons are similar, the diagonals drawn from homologous vertices divide them **into the same number of triangles, similar each to each, and similarly** placed. B Hypothesis. ABCDEF and GHKMNO are similar polygons, and from the homologous vertices are... | |
| Webster Wells - Geometry - 1899 - 424 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. A. Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B',... | |
| Harvard University - Geometry - 1899 - 39 pages
...sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they can be decomposed **into the same number of triangles, similar each to each and similarly** placed. THEOREM VII. The perimeters of two similar polygons are in the same ratio as any two corresponding... | |
| Edward Brooks - 1901 - 278 pages
...DH2 = ~CG2 : FH\ Therefore, A ABC : A DEF => Z<S 2 : UE 2 = UG* : TH\ PROPOSITION XXIX. — THEOREM. **Similar polygons may be divided into the same number...of triangles, similar each to each, and similarly** placed. Given— Let ,45 CUE and FGHIK be two similar polygons, hav- \ ./' ..-•? ing the angle A... | |
| Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...on. Why? Why ? CONVERSELY. If the diagonals drawn from one vertex in each of two polygons divide them **into the same number of triangles, similar each to each and similarly** placed, the two polygons are similar. EXERCISES 1. State the theorem in the first chapter analogous... | |
| American School (Chicago, Ill.) - Engineering - 1903
...polygons are similar, (article 173.) THEOREM LVII. 180. Conversely, two similar polygons may be decomposed **into the same number of triangles, similar each to each and similarly** placed. Let E and E' be homologous vertices of the similar polygons A — E and A' — E', and draw... | |
| Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...therefore similar. PROPOSITION MX. THEOREM 329. If two polygons are similar, they may be separated **into the same number of triangles, similar, each to each, and similarly** placed. B D £' • D' Given the similar polygons ABCDE and A'B'ffjyW, divided into triangles by the... | |
| |