 If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',...  Elements of Geometry and Trigonometry: With Notes - Page 73by Adrien Marie Legendre - 1828 - 316 pagesFull view - About this book
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. B E' D ED Hyp. In the polygons ABCDE and A'BC'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...respectively parallel, or respectively perpendicular, are similar. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...each to each and similarly placed, the polygons are similar. 171. Theorem X. (Converse of Theo. IX.) Two similar polygons are composed of the same number of triangles similar each to each and similarly placed. 172. Theorem XI. The ratio of the perimeters of two similar polygons equals the ratio of similitude... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...(prolonged), are equal.] 166 BOOK III PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and, similarly placed. H B Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI,... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...(Theorem LI.) BG_AB_AC..BC Therefore inerefore, _ THEOREH LVI. 179. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. In the polygons A — E and A' — E', the triangle ABE will be similar to A' B' E', BCE to... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...§351 § 351 Ax. 1 §357 BOOK III. PLANE GEOMETRY. PROPOSITION XXVI. THEOREM. 366. CONVERSELY : If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB,... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...AA CD and A'G'D' are similar. Art. 327. PROPOSITION XX. THEOREM (CONVERSE OF PROP. XIX) 330. // two polygons are composed of the same number of triangles, similar, each to each, and similarly placed , the polygons are similar. B D Given the two polygons ABCDE and A'B'C'D'W, In which the A ABC,... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...similar. Art. 327. BOOK III. PLANE GEOMETRY PROPOSITION XX. THEOREM (CONVERSE OF PROP. XIX) 330. // two polygons are composed of the same number of triangles, similar, each to each, and similarly placed, the polygons are similar. E' Given the two polygons ABCDE and A'B'C'D'B', in which the A ABC,... | |
 | George Clinton Shutts - 1905 - 260 pages
...intersecting lines is divided at the point into two equal parts. PROPOSITION XXII. 307. Theorem. // two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Let the polygons ABC, etc., and A'B'C', etc., be composed of the... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...number of similar triangles, similarly placed. Const. Therefore the polygons are similar. " If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar." § 362 MISCELLANEOUS EXERCISES PROBLEMS OF 'CONSTRUCTION 777 To... | |
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