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" Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. "
Elements of Geometry and Trigonometry: With Notes - Page 74
by Adrien Marie Legendre - 1830 - 316 pages
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Plane and Solid Geometry

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...
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Schultze and Sevenoak's Plane and Solid Geometry

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',...
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Schultze and Sevenoak's Plane Geometry

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',...
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Plane Geometry

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...
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Plane Geometry

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...
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Plane Geometry

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...
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Plane and Solid Geometry

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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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...the corresponding vertices E and Q, instead of the diagonals from A and M. 138. Theorem. — If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. L23° 'BMN Hypothesis. Polygons ABCD ••• and MNOP •••...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...B AF + BD~ + CE = AE + BF2 + CD . " D PROPOSITION XV. THEOREM 293. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Hypothesis. AA EB ~ A A'E'B' ; A EBD ~ A .E'B'D' ; ABCD-AB'C'D'. The triangles are similarly...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...proportional between the whole hypotenuse and the adjacent segment. 412. If two polygons are similar, they are composed of the same number of triangles, similar each to each and similarly placed. 415. The perimeters of two similar polygons are to each other as any two homologous sides....
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