| 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... | |
| 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... | |
| 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',... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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