 | John Reynell Morell - 1875 - 220 pages
...like manner the similitude of the other triangles. Therefore the polygons ABCDE, A' B' C' D' E' are decomposed into the same number of triangles, similar each to each, and similarly placed. COROLLARY. — The homologous diagonals of two similar polygons are proportional to the homologous... | |
 | William Chauvenet - Geometry - 1875 - 390 pages
...similarity (24). PROPOSITION XI.— THEOREM. 39. Conversely, two similar polygons may be decomposed into lhe same number of triangles similar each to each and similarly placed. Let ABCD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and A', let diagonals... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...EF2. Therefore similar triangles, etc. PROPOSITION XXVI. THEOREM. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK be two similar polygons; they may be divided into the same number of similar... | |
 | George Anthony Hill - Geometry - 1880 - 332 pages
...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 ; regular,... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...we can prove that A DBC is similar to A KGH. 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. THEOREM... | |
 | 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 triangles,... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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, C to H, and... | |
 | George Anthony Hill - 1886 - 368 pages
...Hence we arrive at the following useful theorem : — Theorem I. — If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. The converse theorem is also true. State it. If each side of a polygon is... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...to each and similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...to each and similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to... | |
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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. 
