 | 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,... | |
 | 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... | |
 | 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... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 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... | |
 | Edward Brooks - Geometry, Modern - 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 - 462 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 - 390 pages
...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 - 1911 - 553 pages
...SIMILAR POLYGONS' PROPOSITION XIX. THEOREM 329. If tico polygons are similar, they may be separated into the same number of triangles , similar, each to each, and similarly placed. ED E1 D' Given the similar polygons ABODE and A'B'C'D'E', divided into triangles by the diagonals... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...perpendicular, each to each, the triangles are similar. 329. // two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. 342. In a right triangle, I. The altitude to 'he hypotenuse is a mean proportional between... | |
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Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
