| George Bruce Halsted - Geometry - 1886 - 394 pages
...line can be cut only it a single point into external segments having a given ratio.) 516. COROLLARY. **Similar polygons may be divided into the same number of triangles similar** and similarly placed. For if, with their corresponding sides parallel, one of the polygons were placed... | |
| William Chauvenet - Geometry - 1887 - 331 pages
...^. = = = - = = t PROPOSITION VII.—THEOREM. 23. Conversely, two similar polygons may be decomposed **into the same number of triangles similar each to each and similarly** placed. Let AH CD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and... | |
| James Wallace MacDonald - Geometry - 1889 - 63 pages
...triangles whose sides are parallel or perpendicular are similar. Proposition V. A Theorem. 210. Two **similar polygons may be divided into the 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... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...triangles whose sides are parallel or perpendicular are similar. Proposition V. A Theorem. 210. Two **similar polygons may be divided into the 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... | |
| George Albert Wentworth - 1889 - 270 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,... | |
| 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... | |
| Edward Albert Bowser - Geometry - 1890 - 414 pages
...equiangular and having their hoinohgous sides PLANE GEOMETRY. 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 AB0DE, A'B'C'D'E' be two similar polygons divided into AS by the diagonals AC, AD,... | |
| Edward Albert Bowser - Geometry - 1890 - 393 pages
...homologous sides 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... | |
| 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... | |
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...similar polygons, and draw the conclusion. PROPOSITION XX. THEOREM. 237. Converse of Prop. XIX. Two **similar polygons may be divided into the same number of triangles, similar each to each and similarly** placed. C' Let the polygons ABC DEF and A' B' C' D' E' I" be similar, and let all possible diagonals... | |
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