 | 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, William Elwood Byerly - 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 - 80 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 - 276 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 - 420 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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FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
