| Mathematics - 1898 - 228 pages
...center, the nearer is the greater. 3. Define similar polygons, similar sectors, similar segments. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 4. The areas of similar segments have the same ratio as the squares... | |
| Webster Wells - Geometry - 1898 - 250 pages
...homologous base of a similar triangle is PROI-. XX. THEOREM. 266. Tiro polygons are similar irhen the;/ 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... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...of their sides is a parallelogram. PROPOSITION XV. THEOREM. 224. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. A Let ABCDE and A'B'C'D'E' be two polygons composed of the same number of similar triangles... | |
| George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...§351 Ax. 1 § 357 QEO BOOK III. PLANE GEOMETRY. 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,... | |
| Education - 1901 - 814 pages
...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, similar each to each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid... | |
| George Albert Wentworth - Geometry - 1899 - 500 pages
...E'C'D' are similar. §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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
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