 | Yale University - 1898 - 212 σελίδες
...inscribed, escribed, and circumscribed circles of any triangle. 3. (a) Two polygons are similar when composed of the same number of triangles, similar each to each and similarly placed, (b) When the areas of two similar polygons are in the ratio of in to n, in what ratio are the homologous... | |
 | 1898 - 228 σελίδες
...inscribed, escribed, and circumscribed circles of any triangle. 3. (a) Two polygons are similar when composed of the same number of triangles, similar each to each and similarly placed, (b) When the areas of two similar polygons are in the ratio of m to n, in what ratio are the homologous... | |
 | Webster Wells - 1898 - 264 σελίδες
...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. 4 Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B', and E'C'.... | |
 | George Albert Wentworth - 1899 - 498 σελίδες
...351 § 351 Ax. 1 §357 PED BOOK III. PLANE GEOMETRY. PROPOSITION XXVI. THEOREM. 366. CONVERSELY: If two polygons are composed of the same number of triangles,...each, and similarly placed, the polygons are similar. B' In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, BEC, CEB be similar, respectively,... | |
 | 1901 - 814 σελίδες
...exterior point are 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,...each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid is equal to ... 5 State the ratio... | |
 | George Albert Wentworth - 1899 - 278 σελίδες
...351 §351 Ax. 1 § 357 QBIX BOOK III. PLANE GEOMETRY. PROPOSITION XXVI. THEOREM. 366. CONVERSELY: If two polygons are composed of the same number of triangles,...each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively,... | |
 | Webster Wells - 1899 - 450 σελίδες
...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'.... | |
 | Webster Wells - 1899 - 424 σελίδες
...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'.... | |
 | George Albert Wentworth - 1899 - 246 σελίδες
...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... | |
 | George Albert Wentworth - 1899 - 272 σελίδες
...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... | |
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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. 
