 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...triangles similar each to each, and similarly situated. Let ABCDE, FGHIK be two similar polygons ; they may be divided into the same number of triangles similar each to each, arid similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I.... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...triangles similar each to each, and similarly situated. Let ABCDE, FGHIK be two similar polygons; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I. The two polygons being similar,... | |
 | John Reynell Morell - 1875 - 220 pages
...the base BC is divided at the points F, G, H. THEOREM XII. Two similar polygons can fee decomposed into the same number of triangles, similar each to each, and similarly placed. Let there be two similar polygons ABCDE, A' B' C' ' D' E'. From their homologous summits draw... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...are similar each to each, and similarly situated. Cor. Conversely, if two polygons are composed of the same number of triangles, similar each to each, and similarly situated, the polygons are similar. For, because the triangles are similar, the angle ABC is equal to FGH ; and... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...other as AB is to ab. Hence, also, ABC : abc = AD- : ad2. SIMILAR POLYGONS. XXVII. • Theorem. Two similar polygons may be divided into the same number of triangles similar each to each. HYPOTII. ABODE and abode are similar polygons, divided into triangles by diagonals drawn from the vertices... | |
 | George Anthony Hill - Geometry - 1880 - 332 pages
...angles of a polygon = 180° X the number of bides less two. 4. Two polygons are equal, if they can be divided into the same number of triangles, similar each to each, and similarly placed. 5. A polygon is equilateral, if its sides are equal ; equiangular, if its angles are equal... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...Likewise we can prove that A DB С is similar to A KGS. QED 279. COR. — Two similar polygons can be divided into the same number of triangles similar each to each and similarly placed, by drawing lines to their vertices from any two homologous points. ELEMENTS OF PLANE GEOMETRY.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...the area of the first than that of the second? An*. 2$. THEOREM IX. Similar polygons may be resolved into the same number of triangles, similar, each to each, and similarly placed. Let P and P' be two similar polygons; then, can they be resolved into the same number of similar... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...the first proportion (B. II., P. IV.), we have, ABC : DEF : : ^C* : DF2. PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number...of triangles, similar, each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons, the angle A being equal to the angle F, B to G,... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...line can be cut only at a single point into external segments having a given ratio.) 516. COROLLARY. Similar polygons may be divided into the same number of triangles similar and similarly placed. For if, with their corresponding sides parallel, one of the polygons were placed... | |
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Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
