 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...divides the opposite side 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... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...ABD and A'B'D' are similar by § 237.) PROP. XVIII. THEOREM 246. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. A A' or Draw polygon ABCDE; from E draw diagonals EC and EB. Construct A E'D'C' similar to... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...ABD and A'B'D' are similar by § 237.) PROP. XVIII. THEOREM 246. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. A A' DlDraw polygon ABCDE; from E draw diagonals EC and EB. Construct A E'D'C' similar to A... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...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, and similarly placed, the polygons are similar. 295. Theorem X. The areas of similar polygons have the same ratio... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...§288 §282 §282 Ax. 2 §282 §282 Ax. 8 QED SIMILAR POLYGONS PROPOSITION XIX. THEOREM 173 293. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. AB A' B' Given two polygons ABCDE and A'B'C'D'E' composed of the... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...fence SCALE or RODS around the farm, if the fencBOOK III PROPOSITION XXII. THEOREM 189 438. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Given polygons ABCDE and FGHIJ with A ABC A ACD ~ A FBI, A ADE ~... | |
 | Geometry, Plane - 1911 - 192 pages
...centre, the nearer is the greater. 3. Define similar polygons, similar sectors, similar segments. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 4. The areas of similar segments have the same ratio as the squares... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...can be shown that the other 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... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
.../*', and b : b' = c : c'. .-. c:c' = /i : h'. 5. .-. AU ~ A f/'. 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. c E Given the polygons Pand P', with the triangle T similar to the... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...triangles any two homologous altitudes have the same ratio as any two homologous sides. 438. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 443. In a right triangle, if the altitude upon the hypotenuse is... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
