 | George Albert Wentworth - Geometry - 1899 - 500 pages
...triangles CED and CAB are similar. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. BC B' C Let the polygons ABCDE and A'B'C'D'E' be similar. From two homologous vertices, as E and E',... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...CAB are similar. SIMILAR POLYGONS. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed, of the same number of triangles, similar each to each, and similarly placed. E BC Let the polygons ABCDE and A'B'C'D'B' be similar. From two homologous vertices, as E and E', draw... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...homologous base of a similar triangle is PROP. XX. THEOREM. 266. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Given, in polygons AC and A'C', A ABE similar to A A' B'E', A BCE to AB'C'E', and A CDE to A C'D'E'.... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...homologous base of a similar triangle is PROP. XX. THEOREM. 266. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. V Given, in polygons AC and A'C', A ABE similar to A A'B'E', ABCE to AB'C'E', and A CDE to A C'D'E'.... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...respectively parallel, or respectively perpendicular, are similar. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse... | |
 | 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... | |
 | 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... | |
 | 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 - 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... | |
 | 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 IV, proving the equality... | |
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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. 
