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" FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. "
New Elementary Geometry: With Practical Applications : a Shorter Course Upon ... - Page 88
by Benjamin Greenleaf - 1874 - 176 pages
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...demonstration. PROPOSITION XXIII. 309. Theorem. CONVERSE or PROPOSITION XXII. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. GA Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...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,...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...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,...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 392 pages
...A'B' = BC : B'C' = AC : A'C' = CD : C'D', etc. ; 149 PROPOSITION XVIII. THEOREM. 295. Conversely, two similar polygons may be divided into the same number of triangles, similar to each other and similarly placed. Given: ABCDE, or P, and A'B'C'D'E', or P', two similar polygons;...
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Plane Geometry

George D. Pettee - Geometry, Plane - 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...
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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...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...B'E' B'C ' BE BC In 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...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 264 pages
...proportional. PROP. XXI. THEOREM. 267. (Converse of Prop. XX.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. 4 Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B',...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...BE, and CF meet in a point. Therefore, etc. QBD Proposition XII 309. Draw two polygons such that they may be divided into the same number of triangles, similar, each to each, and similarly situated. How do the homologous angles of these polygons compare in size ? How do the ratios of any two pairs...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...Bid : B 2 C 2 = = r. .'. A^ + JBiCi + :A 2 B 2 + B 2 C 2 + = r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and Of coincide, and the figures can be placed having 0 within each. The triangles AiOB...
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