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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. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',... "
Elements of Geometry and Trigonometry: With Notes - Σελίδα 75
των Adrien Marie Legendre - 1828 - 316 σελίδες
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 σελίδες
...A ADE and 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...

Solid Geometry, Τόμοι 6-9

George Albert Wentworth - 1902 - 218 σελίδες
...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...

Plane Geometry by the Suggestive Method

John Alton Avery - 1903 - 122 σελίδες
...each to each 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...

Elements of Plane and Solid Geometry

Alan Sanders - 1903 - 384 σελίδες
...(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,...

Mathematics, mechanics, heat

American School (Chicago, Ill.) - 1903
...(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...

Plane and Solid Geometry

George Albert Wentworth - 1904 - 473 σελίδες
...§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,...

PLANE AND SOLID GEOMETRY

FLETCHER DURELL. PH.D. - 1911
...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,...

Plane Geometry

Fletcher Durell - 1904 - 372 σελίδες
...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,...

Plane Geometry Suggestive Method

George Clinton Shutts - 1905
...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...

Plane and Solid Geometry

Isaac Newton Failor - 1906 - 418 σελίδες
...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...




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