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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 and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...one' of the given lines (Art. 226.) PROPOSITION XIX. THEOREM. * 236. // two polygons are com,posed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Let the polygons AB CD EF and A' B' C' D E' F be composed of the same number...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...is, the perimeters have the ratio r, which is the ratio of the corresponding sides. 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and 0' coincide, the figures can be placed having O within each, and the triangles AiOBi, A2OB2...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...is, the perimeters have the ratio r, which is the ratio of the corresponding sides. 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and 0' coincide, the figures can be placed having 0 within each, and the triangles A1OB1, A2OB2...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...parallel or perpendicular. PROPOSITION XVII. THEOREM. 294. Two polygons are similar if composed of the same number of triangles similar each to each and similarly placed. A, U, Given: In polygons P and P', triangles A ED, ADC, ACB, similar to triangles A'E'D', A'D'C', A'C'B',...
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Plane Geometry

George D. Pettee - Geometry, Modern - 1896 - 272 pages
...homologous sides. S1MILAK FIG USES PROPOSITION XIX 105 Theorem. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. EDS Appl. Prove M sim. N, etc., in given sim Dem. B = 2 [in sim. ] AB = BC 1H ~ 23 M and N sim....
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...segments upon two parallels, they pass through a common point. 331. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 332. If two polygons are similar, they are composed of the same number of...
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Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 214 pages
...given circle a regular polygon similar to a given regular polygon. 6. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. The University of Chicago, September, 1896. TIME ALLOWED, ONE HOUR AND FIFTEEN...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...QED EXERCISE. PROPOSITION XXVII. THEOREM. 272. CONVERSELY—Two si?nilar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. Given — ABCDE and FGHKL two similar polygons. To Prove— A-IBC similar to &FGH, &ACD to &FHK, and...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...homologous sides are in the ratio of similtude AB : HI. 271. THEOREM. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. 272. THEOREM. If two polygons are similar, they may be resolved into the...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...like manner, AB BC CD DE EA A'B' B'C CD' D'E' E'A' QED 225. COB. Conversely, two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. PROPOSITION XVI. THEOREM. 226. The perimeters of two similar polygons have the name ratio as any two...
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