 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...(Theorem LI.) BG_AB_AC..BC Therefore inerefore, _ THEOREH LVI. 179. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. In the polygons A — E and A' — E', the triangle ABE will be similar to A' B' E', BCE to... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...(prolonged), are equal.] 166 BOOK III 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. H B Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI,... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...similar. Art. 327. BOOK III. PLANE GEOMETRY PROPOSITION XX. THEOREM (CONVERSE OF PROP. XIX) 330. // two polygons are composed of the same number of triangles, similar, each to each, and similarly placed, the polygons are similar. E' Given the two polygons ABCDE and A'B'C'D'B', in which the A ABC,... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...§351 § 351 Ax. 1 §357 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,... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...AA CD and A'G'D' are similar. Art. 327. PROPOSITION XX. THEOREM (CONVERSE OF PROP. XIX) 330. // two polygons are composed of the same number of triangles, similar, each to each, and similarly placed , the polygons are similar. B D Given the two polygons ABCDE and A'B'C'D'W, In which the A ABC,... | |
 | George Clinton Shutts - 1905 - 260 pages
...intersecting lines is divided at the point into two equal parts. PROPOSITION XXII. 307. Theorem. // two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Let the polygons ABC, etc., and A'B'C', etc., be composed of the... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...side ; then 40 - x = the other side. PLANE GEOMETRY — BOOK III PROPOSITION XXIV. THEOREM 362 If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. HYPOTHESIS. The & ABC, ACD, and ADE are similar respectively to the... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...number of similar triangles, similarly placed. Const. Therefore the polygons are similar. " If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar." § 362 MISCELLANEOUS EXERCISES PROBLEMS OF 'CONSTRUCTION 777 To... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...inches; what is the radius? Ans. 13i in. OTHER SIMILAR POLYGONS 32. Two polygons are similar when they are composed of the same number of triangles similar each to each and similarly placed. Thus, in Fig. 25, the polygons ABCDE and A' B> C1 D> E> are composed of the same number of... | |
 | Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...homologous altitudes of two similar triangles equals the ratio of similitude of the triangles. 89. If two polygons are composed of the same number of triangles similar each to each and similiarly placed, the polygons are similar. 90. Converse of 89. 91. The ratio of the perimeters of... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
