 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...triangle similarly situated in , Proposition 142. Theorem. 176. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Since the homologous A are either homologous A of similar A, or else the sums of such A, the -polygons... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 309 SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ; then construct... | |
 | Harvard University - Geometry - 1899 - 39 pages
...sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they can be decomposed into the same number of triangles, similar each to each and similarly placed. THEOREM VII. The perimeters of two similar polygons are in the same ratio as any two corresponding... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...= r. .-. AiBi + B1C1 + :A 2 B 2 + B 2 C 2 + =r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and O" coincide, and the figures can be placed having 0 within each. The triangles AiOBi, A^OB... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
....: AlBi + Bid + ..... :A2B2 + B2C2 + ..... = r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For O and 0" coincide, and the figures can be placed having 0 within each. The triangles AiOBi, A2OB2... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. E' D' ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Arthur Schultze - 1901 - 260 pages
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. ED Hyp, In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', D A CDE ~ A C'D'E'.... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...circles. Draw the two common chords. PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and .similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and be similarly... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. B E' D ED Hyp. In the polygons ABCDE and A'BC'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...Why? Why ? CONVERSELY. If 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, the two polygons are similar. EXERCISES 1. State the theorem in the first chapter analogous to Proposition... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
