 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...homologous sides proportional." § 349 162 PROPOSITION XXV. THEOREM 363 If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. HYPOTHESIS. The polygons ABCDE and A'B'C'D'E' are sinular. CONCLUSION. The & ABC, ACD, and ADE are... | |
 | Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...altitudes of two similar triangles equals the ratio of similitude of the triangles. 89. If two polygons are composed of the same number of triangles similar each to each and similiarly placed, the polygons are similar. 90. Converse of 89. 91. The ratio of the perimeters of... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...the shortest side of the less. 327. THEOREM. If two polygons are similar, they may be decomposed into the same number of triangles similar each to each and similarly placed. Given : Similar polygons BE and B'E' ' . To Prove : A ABC similar to A A'B'C'; AACD similar to A A'C'D';... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...of the less. PLANE GEOMETRY 327. THEOREM. If two polygons are similar, they may be decomposed into the same number of triangles similar each to each and similarly placed. Given : Similar polygons BE and B'E'. To Prove : A ABC similar to A A'B'C'; AACD similar to A A'C'D'; AA... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...(Rt. A ABD and A'B'D' are similar by § 237.) PROP. XVIII. THEOREM 246. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. A A' DlDraw polygon ABCDE; from E draw diagonals EC and EB. Construct A E'D'C' similar to A EDC, sides... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...(Et. A ABD and A'B'D' are similar by § 237.) PROP. XVIII. THEOREM 246. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. A A' Draw polygon ABCDE; from ^draw diagonals EO and EB. Construct A E'D'C' similar to A EDC, sides... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...opposite side externally into segments proportional to the sides of the angle. 355. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 356. If two polygons are similar, they can be separated into the same number... | |
 | Webster Wells - Geometry - 1908 - 329 pages
...C'D1' PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous ; and diagonals EB, EC, E'B',... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...similarly placed, the polygons are similar. 356. If two polygons are similar, they can be separated into the same number of triangles, similar each to each and similarly placed. 357. The perimeters of two similar polygons are in the same ratio as any two corresponding sides. 359.... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...= = PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may lie decomposed into the same number of triangles, similar each to each, and similarly placed. 4 Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous ; and diagonals EB, EC,... | |
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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. 
