 | William James Milne - Geometry - 1899 - 398 pages
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 301i SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 309 SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ;... | |
 | William James Milne - Geometry - 1899 - 404 pages
...PLANE GEOMETRY. — BOOK IV. Proposition XII 309. Draw two polygons such that they may be divided into the same number of triangles, similar, each to each, and similarly situated. How do the homologous angles of these polygons compare in size? How do the ratios of any two pairs... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...similar manner 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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. 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... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...circles. Draw the two common chords. 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. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...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... | |
 | Arthur Schultze - 1901 - 260 pages
...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. ED Hyp, In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', D A CDE ~... | |
 | 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... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...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... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
