 If two polygons are similar, they can be divided into the same number of triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed,...  Plane and Solid Geometry, Suggestive Method - Page 376by George Clinton Shutts - 1913 - 476 pagesFull view - About this book
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...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, EEC, CED... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...and CAB are similar. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. BC B' C Let the polygons ABCDE and A'B'C'D'E' be similar. From two homologous vertices, as E and E',... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...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 equal to... | |
 | 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 to Proposition... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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. E' D' ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Arthur Schultze - 1901 - 260 pages
...similar. (Ax. 1.) PROPOSITION XXVII. THEOREM (295) 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. E , D Hyp. In the polygons ABCDE and A'B'C'D'E', D A BCE ~ A B'C'E', A CDE ~ A C'D'E'. To prove polygon... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...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 ~ A C'D'E'.... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...the two common chords. 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. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and be similarly... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...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 the hypotenuse:... | |
 | 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 the diagonals... | |
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