 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 be similar, respectively, to the triangles A'E'B',...  Elements of Geometry and Trigonometry: With Notes - Page 73by Adrien Marie Legendre - 1828 - 316 pagesFull view - About this book
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...triangles any two homologous altitudes have the same ratio as any two homologous sides. 438. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 443. In a right triangle, if the altitude upon the hypotenuse is... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
.../*', and b : b' = c : c'. .-. c:c' = /i : h'. 5. .-. AU ~ A f/'. PROPOSITION XVI. THEOREM 413. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. c E Given the polygons Pand P', with the triangle T similar to the... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...can be shown that the other triangles are similar, each to each. PROPOSITION XVI. THEOREM 413. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Given the polygons Pand P', with the triangle T similar to the triangle... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...§288 §282 §282 Ax. 2 §282 §282 Ax. 8 QED SIMILAR POLYGONS PROPOSITION XIX. THEOREM 178 293. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. ABA Given two polygons ABODE and A'B'C'D'E' composed of the triangles... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...similar. ' (303) (Ax. 1.) (309) PROPOSITION XXV. THEOREM Q. E D. 314. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Given in the polygons ABCDE and A'B'C'D'E', AABE~ AA'B'E', ABCE ~ AB'C'E', A CDE ~ A C'D'E',... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...are similar. (Ax. 1.) (309) PROPOSITION XXV. THEOREM Q. E D. 314. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Given in the polygons ABCDE and A'B'C'D'E', AABE~ AA'B'E', ABCE ~ AB'C'E', A CDs ~ A C'D'E',... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...A CDO . Why? Why? Why? Why? Why? Why? Why? ,AC'D'O', etc. 178 SIMILAR POLYGONS 426. THEOREM. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. B FIG. 197. Given the polygons ABCDE •.. and A'B'C'D'E' ... composed... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...19 to 40, p. 291, can be studied now. PROPOSITION XV. THEOREM 293. Two polygons arc similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Hypothesis. A AEB ~ A A'E'B' ; A ESD ~ A E'B'D' ; A BCD ~ A B'C'D'. The triangles are similarly... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 336 pages
...AC BC DC AD DB (1) 13 12 (2) 12 3| (3) 16 4 (4) 20 12 (5) 30 50 SIMILAR POLYGONS 441. Two polygons composed of the same number of triangles, similar each to each and similarly placed, are similar polygons. 442. Problem. Construct a polygon similar to a given polygon having given... | |
 | William Betz - Geometry - 1916 - 536 pages
...Why? 6. In like manner it can be shown that the other triangles are similar, each to each. 413. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. c; £ Given the polygons .Pand F, with the triangle T similar to... | |
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