| Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...perpendicular, each to each, the triangles are similar. 329. // two polygons are similar, they may be separated **into the same number of triangles, similar, each to each, and similarly** placed. 342. In a right triangle, I. The altitude to 'he hypotenuse is a mean proportional between... | |
| Fletcher Durell - Geometry - 1911 - 553 pages
...SIMILAR POLYGONS' PROPOSITION XIX. THEOREM 329. If tico polygons are similar, they may be separated **into the same number of triangles , similar, each to each, and similarly** placed. ED E1 D' Given the similar polygons ABODE and A'B'C'D'E', divided into triangles by the diagonals... | |
| George Clinton Shutts - 1905 - 260 pages
...demonstration. OD PROPOSITION XXIII. 309. Theorem. CONVERSE OF PROPOSITION XXII. Two similar polygons can **be divided into the same number of triangles, similar each to each and similarly** placed. GA G' A' Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...find the shortest side of the less. 327. THEOREM. If two polygons are similar, they may be decomposed **into the same number of triangles similar each to each and similarly** placed. Given : Similar polygons BE and B'E' ' . To Prove : A ABC similar to A A'B'C'; AACD similar... | |
| Edward Rutledge Robbins - Geometry - 1907 - 412 pages
...side of the less. PLANE GEOMETRY 327. THEOREM. If two polygons are similar, they may be decomposed **into the same number of triangles similar each to each and similarly** placed. Given : Similar polygons BE and B'E'. To Prove : A ABC similar to A A'B'C'; AACD similar to... | |
| Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...similarly placed. IJ Given: ABCDEF and GHUKL, two similar polygons. To Prove : That the polygons can **be divided into the same number of triangles, similar each to each and similarly** placed. Proof : From the corresponding vertices A and G draw all diagonals possible. Then A CAB ~ A... | |
| Webster Wells - Geometry, Plane - 1908 - 206 pages
...manner, = = PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may lie decomposed **into the same number of triangles, similar each to each, and similarly** placed. 4 Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous ; and diagonals... | |
| Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...(Why?) THEOREM XVII (Converse of Theorem XVI) 356. If two polygons are similar, they can be separated **into the same number of triangles, similar each to each and similarly** placed. Given : ABCDEF and GHIJKL, two similar polygons. To Prove : That the polygons can be divided... | |
| Webster Wells - Geometry - 1908 - 338 pages
...like manner, PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may be decomposed **into the same number of triangles, similar each to each, and similarly** placed. Z» Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous; and diagonals... | |
| Education - 1909
...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... | |
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