 | George Albert Wentworth - Geometry - 1899 - 498 pages
...CAB are similar. 156 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. BG **' Let the polygons ABCDE and A'B'C'D'E' be similar. From two homologous vertices, as E and E',... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...to the 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... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...and 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 - 450 pages
...the 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'.... | |
 | Education - 1901 - 814 pages
...equal, and make equal angles with the line ; the point to the center. 3 Prove that if two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid is equal... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...351 Ax. 3 §351 § 351 Ax. 1 §357 QED PROPOSITION XXVI. THEOREM. 366. CONVERSELY: If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, BEC, CED... | |
 | 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 - 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... | |
 | 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... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...proportional. PROP. XXI. THEOREM. 267. (Converse of Prop. XX.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. A. Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B', and... | |
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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. 
