 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 143by Arthur Schultze - 1901Full view - About this book
 | Harvard University - Geometry - 1899 - 39 pages
...sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they can be decomposed into the same number of triangles, similar each to each and similarly placed. THEOREM VII. The perimeters of two similar polygons are in the same ratio as any two corresponding... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...A'C'D'. In like manner, A ADE and A'D'E' are similar. (Ax. 1.) (295) PROPOSITION XXVII. THEOREM QED 304. Two polygons are similar if they are composed...and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'. To prove polygon ABCDE ~ polygon A'B'C'D'E'. HINT. — The polygons are mutually... | |
 | Arthur Schultze - 1901 - 392 pages
...A A'B'O, BC CD and B'C' C'D'' BC = AC . B'C' A'C'' . CD AC (Ax. 1.) C'D' A'C' .-. A ACD ~ A A'C'D'. (295) In like manner, A ADE and A'D'E' are similar....triangles, similar each to each, and similarly placed. D E " D Hyp, In the polygons ABCDE and A'B'C'D'E', AABE~AA'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...ABC ~ A A'B'C', BC CD B'C' C'D'' and BC = B'C' ~ A'C'' CD AC ' ' C'D' A'C' - .'. A ACD ~ A A' C'D'. (295) In like manner, A ADE and A'D'E' are similar....triangles, similar each to each, and similarly placed. E' D' ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...A'C'' AC ' C'D' A'C' .-. A ACD ~ A A'C'D'. In like manner, A ADE and A'D'E' are similar. (Ax. 1.) (295) QED PROPOSITION XXVII. THEOREM 304. Two polygons are...triangles, similar each to each, and similarly placed. D E _ D Hyp. In the polygons ABCDE and A'B'C'D'E', AABE~AA'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...circle intersecting the two given circles. Draw the two common chords. 167 PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the-...triangles, similar each to each, and similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively ' to the A GHI, GJI, JLI, and LMI, and be... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...we may prove that A AED is similar to A FKI. Therefore, etc. Con. — CONVERSELY : If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the two polygons are similar. This may be readily proved, the demonstration being almost the converse... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...Why? Why ? CONVERSELY. If the diagonals drawn from one vertex in each of two polygons divide them into the same number of triangles, similar each to each and similarly placed, the two polygons are similar. EXERCISES 1. State the theorem in the first chapter analogous to Proposition... | |
 | 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:... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...intersection of 3 common chords (prolonged), are equal.] 166 BOOK III PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the...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... | |
| |
