 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...DEF => Z<S 2 : UE 2 = UG* : TH\ PROPOSITION XXIX. — THEOREM. Similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. Given— Let ,45 CUE and FGHIK be two similar polygons, hav- \ ./' ..-•? ing the angle A equal to... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 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:... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...and similarly placed, the polygons are similar. 171. Theorem X. (Converse of Theo. IX.) Two similar polygons are composed of the same number of triangles similar each to each and similarly placed. 172. Theorem XI. The ratio of the perimeters of two similar polygons equals the ratio of similitude... | |
 | 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, and be... | |
 | 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 B' C' E',... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...are similar. Art. 327. BOOK III. PLANE GEOMETRY PROPOSITION XX. THEOREM (CONVERSE OP PROP. XIX) 330. If two polygons are composed of the same number of...each, and similarly placed, the polygons are similar. D Given the two polygons ABCDE and A'B'C'D'E', in which the A ABC, ACD, AH 'E are similar, respectively,... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...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. E BC Let the polygons ABCDE and AU'C'DTS' be similar. From two homologous vertices, as E and E', draw... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...SIMILAR POLYGONS' PROPOSITION XIX. THEOREM 329. If tico polygons are similar, they may be separated into the same number of triangles , similar, each to each, and similarly placed. ED E1 D' Given the similar polygons ABODE and A'B'C'D'E', divided into triangles by the diagonals AC,... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...each to each, the triangles are similar. 329. // two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. 342. In a right triangle, I. The altitude to 'he hypotenuse is a mean proportional between the segments... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...therefore similar. PROPOSITION MX. THEOREM 329. If two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. B D £' • D' Given the similar polygons ABCDE and A'B'ffjyW, divided into triangles by the diagonals... | |
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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. 
