 If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar.  New Plane Geometry - Page 117by Webster Wells - 1908 - 174 pagesFull view - About this book
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...externally into segments proportional to the sides of the angle. 355. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 356. If two polygons are similar, they can be separated into the same number... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...the given triangle? (Two cases.) 293. Theorem VIII. // two polygons are similar, they can be divided into the same number of triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each,... | |
 | Education - 1909 - 720 pages
...equal to one-half of the third side. 2. Demonstrate: If two polygons are similar, they may be separated into the same number of triangles, similar each to each, and similarly placed. 3. Construct a fourth proportional to three given lines. 4. Demonstrate : Of isoperimetria polygons... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 204 pages
...triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 295. Theorem X. The areas of similar polygons have the same ratio as the... | |
 | 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 A' in the... | |
 | 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 A... | |
 | 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', B', C',... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...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, to construct a... | |
 | Geometry, Plane - 1911 - 192 pages
...the segments of each side are incommensurable. 5. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. 6. Two sides and the included angle of a quadrilateral are fixed. If the angle opposite the included... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...triangles are similar, each to each. PROPOSITION XVI. THEOREM 413. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Given the polygons Pand P', with the triangle T similar to the triangle T',... | |
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