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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. "
Plane Geometry - Page 170
by Webster Wells, Walter Wilson Hart - 1915 - 309 pages
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Plane Geometry Suggestive Method

George Clinton Shutts - 1905 - 260 pages
...Complete the demonstration. OD PROPOSITION XXIII. 309. Theorem. CONVERSE OF PROPOSITION XXII. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. GA G' A' Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be drawn...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...find 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';...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...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 PEOBLEMS OF CONSTRUCTION 777 To divide one...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...A'B' QED PLANE GEOMETRY — BOOK III PROPOSITION XXIV. THEOREM 362 If two polygons are . composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. HYPOTHESIS. The & ABC, ACD, and ADE are similar respectively to the A A'B'C',...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 634 pages
...radius? Ans. 13i in. OTHER SIMILAR POLYGONS 32. Two polygons are similar when they are composed of the same number of triangles similar each to each and similarly placed. Thus, in Fig. 25, the polygons ABCDE and A' B> C1 D> E> are composed of the same number of similar...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...side 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';...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...each to each and similarly placed. Given : ABCDEF and GHIJKL, two similar polygons. To Prove : That the polygons can be divided into the same number of...triangles, similar each to each and similarly placed. Proof : From the corresponding vertices A and G draw all diagonals possible. Then A CAB ~ A IGH. (...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 206 pages
...manner, = = 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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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 336 pages
...like manner, 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. Z Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous; and diagonals EB, EC,...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...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...
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