If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Plane Geometry - Page 170by Webster Wells, Walter Wilson Hart - 1915 - 309 pagesFull view - About this book
| Arthur Schultze - 1901 - 260 pages
...similar. (Ax. 1.) PROPOSITION XXVII. THEOREM (295) 304. Two polygons are similar if they are composed of **the same number of triangles, similar each to each, and similarly placed.** E , D Hyp. In the polygons ABCDE and A'B'C'D'E', D A BCE ~ A B'C'E', A CDE ~ A C'D'E'. To prove polygon... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of **the same number of triangles, similar each to each, and similarly placed.** B E' D ED Hyp. In the polygons ABCDE and A'BC'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
| George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...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:... | |
| American School (Lansing, Ill.) - Engineering - 1903 - 390 pages
...polygons are similar, (article 173.) THEOREM LVII. 180. Conversely, two similar polygons may be decomposed **into the same number of triangles, similar each to each and similarly placed.** Let E and E' be homologous vertices of the similar polygons A — E and A' — E', and draw the diagonals... | |
| John Alton Avery - Geometry, Modern - 1903 - 136 pages
...into segments proportional to the adjacent sides. 169. Theorem IX. If two polygons are composed of **the same number of triangles, similar each to each and similarly placed,** the polygons are similar. 171. Theorem X. (Converse of Theo. IX.) Two similar polygons are composed... | |
| Alan Sanders - Geometry - 1903 - 396 pages
...(prolonged), are equal.] PROPOSITION XXV. THEOREM 542. Tivo polygons are similar if they are composed of **the same number of triangles, similar each to each, and similarly placed.** Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and be similarly... | |
| 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, 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... | |
| Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...perpendicular, 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... | |
| George Albert Wentworth - Geometry - 1904 - 496 pages
...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... | |
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