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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 Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...D'E' E'A' 270. THEOREM. // the diagonals drawn from one vertex in each of two polygons divide them into the same number of triangles, similar each to each and similarly placed, then the two polygons are similar. B ~ B' , c' JD' E Given the diagonals drawn from the vertices...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...BC CD DE EA 270. THEOREM. // the diagonals drawn from one vertex in each of two polygons divide them into the same number of triangles, similar each to each and similarly placed, then the two polygons are similar. D' E' Given the diagonals drawn from the vertices A and...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...AEF are similar. PROPOSITION XVIII. THEOREM 292. If two polygons are similar, they can be separated into the same number of triangles, similar each to each, and similarly placed. Given two similar polygons ABCDE&nA A'B'C'D'E' with angles A, B, C, D, E equal to angles A',...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...7. By proof. 8. 424, 2. 9. 424, 2. 10. 424, 2. 11. 54, 1. 12. 419. 439. Cor. Any two similar polygons may be divided into the same number of triangles similar each to each and similarly placed. PROPOSITION XXIII. PROBLEM 440. Upon a line homologous to a side of a given polygon, to construct...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...proof. 424, 2. 424, 2. 424, 2. 54 1 at/i ? j.. 419. 439. Cor. Any two similar polygons may be divided into the same number of triangles similar each to each and similarly placed. PROPOSITION XXIII. PROBLEM 440. Upon a line homologous to a side of a given polygon,...
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...1-5. 7. By proof. 8. 424, 2. 9. 424,2. 10. 424, 2. 11. 54,1. 12. 419. 439. Cor. Any two similar polygons may be divided into the same number of triangles similar each to each and similarly placed. PROPOSITION XXIII. PROBLEM 440. Upon a line homologous to a side of a given polygon, to construct...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...in each of the including faces all possible diagonals. The corresponding faces of P and P' are thus divided into the same number of triangles, similar each to each and similarly placed. Why? 2. Let OE and O'E' be two corresponding edges and let OF and OG be the two diagonals including...
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Solid Geometry

George C. Shutts - 1913 - 212 pages
...in each of the including faces all possible diagonals. The corresponding faces of P and P' are thus divided into the same number of triangles, similar each to each and similarly placed. Why? 2. Let OE and O'E' be two corresponding edges and let OF and OG be the two diagonals including...
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...165. Definitions Similar Polygons. Two polygons are said to be similar when each may be decomposed into the same number of triangles similar each to each and similarly placed. Thus, in the figure, the polygons ABCDE and A'B'C'D'E' are similar. For, if we draw the lines...
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Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - Geometry, Plane - 1913 - 272 pages
...165. Definitions. Similar Polygons. Two polygons are said to be similar when each in ay be decomposed into the same number of triangles similar each to each and similarly placed. Thus, in the figure, the polygons ABCDE and A'B'C'D'E' are similar. For, if we draw the lines...
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