 | 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... | |
 | 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 - 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'.... | |
 | 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'.... | |
 | 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:... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...(prolonged), are equal.] PROPOSITION XXV. THEOREM 542. Tivo 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... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...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 B' C' E',... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...into segments proportional to the adjacent sides. 169. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 171. Theorem X. (Converse of Theo. IX.) Two similar polygons are composed... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...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, and be... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
