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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

Arthur Schultze - 1901 - 260 pages
...similar. (Ax. 1.) PROPOSITION XXVII. THEOREM (295) 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. E , D Hyp. In the polygons ABCDE and A'B'C'D'E', D A BCE ~ A B'C'E', A CDE ~ A C'D'E'. To prove polygon...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. B E' D ED Hyp. In the polygons ABCDE and A'BC'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'....
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...or respectively perpendicular, are similar. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse:...
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Mathematics, mechanics, heat

American School (Lansing, Ill.) - Engineering - 1903 - 390 pages
...polygons are similar, (article 173.) THEOREM LVII. 180. Conversely, two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. Let E and E' be homologous vertices of the similar polygons A — E and A' — E', and draw the diagonals...
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Modern - 1903 - 136 pages
...into segments proportional to the adjacent sides. 169. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 171. Theorem X. (Converse of Theo. IX.) Two similar polygons are composed...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...(prolonged), are equal.] PROPOSITION XXV. THEOREM 542. Tivo polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and be similarly...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...SIMILAR POLYGONS' PROPOSITION XIX. THEOREM 329. If tico polygons are similar, they may be separated into the same number of triangles , similar, each to each, and similarly placed. ED E1 D' Given the similar polygons ABODE and A'B'C'D'E', divided into triangles by the diagonals AC,...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...therefore similar. PROPOSITION MX. THEOREM 329. If two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. B D ' • D' Given the similar polygons ABCDE and A'B'ffjyW, divided into triangles by the diagonals...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...perpendicular, each to each, the triangles are similar. 329. // two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. 342. In a right triangle, I. The altitude to 'he hypotenuse is a mean proportional between the segments...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...SIMILAR POLYGONS. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. E BC Let the polygons ABCDE and AU'C'DTS' be similar. From two homologous vertices, as E and E', draw...
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