 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...A'B'C'D'E', homologous vertices being indicated by corresponding letters. Conclusion. The polygons can be divided into the same number of triangles, similar each to each and similarly placed. Construction. Draw BE, BD, B'E', and B'D'. Statement. A ABE ~ A A' B'E' ; A EBD ~ A E'B'D'... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...GEOMETRY: BOOK III THE DECOMPOSITION OF SIMILAR POLYGONS 363. THEOREM XVI. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. c' Given similar polygons P and P' with diagonals drawn from the vertices A and A'. To prove... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...GEOMETRY: BOOK III THE DECOMPOSITION OF SIMILAR POLYGONS 363. THEOREM XVI. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. E> O' Given similar polygons P and P with diagonals drawn from the vertices A and A'. To prove... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...number of sides are similar. Draw diagonals from one vertex in each and prove that the polygons are divided into the same number of triangles, similar each to each and similarly placed. 477. Theorem. The perimeters of two similar regular polygons are to each other as their radii,... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...122. If two polygons are similar, diagonals drawn from two corresponding vertices divide the polygon into the same number of triangles similar each to each and similarly placed. THEOREM 123. The ratio of corresponding altitudes of two similar triangles equals the ratio... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...each. A Given the convex polygon ABCDE similar to the convex polygon A'B'C'D'E'. To prove that these polygons may be divided into the same number of triangles similar each to each and similarly placed. Proof. Draw from two corresponding vertices A and A' all the diagonals possible. Then 4^-.... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...similar to the triangle K'B'C'. Theorem 18 (Converse of Theorem IT) 299. If two convex polygons can be divided into the same number of triangles similar each to each and similarly placed, the polygons are similar. E' E A B' Given the convex polygons ABCDEF and A'B'C'D'E'F' divided... | |
 | Robert Remington Goff - 1922 - 136 pages
...are composed of the same number of triangles, similar each to each, and similarly placed. *286. Two similar polygons may be divided into the same number...of triangles, similar each to each, and similarly placed. *28y. Problem: On a given line corresponding to a side of a given polygon, construct a polygon... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...of two similar polygons have the same ratio as any two homologous sides. 6. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. Proof (Continued) STATEMENTS REASONS 7. r , , - , 7. The homologous sides of similar triangles... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...121. Two polygons are similar if diagonals drawn from two corresponding vertices divide the polygons into the same number of triangles similar each to each and similarly placed. THEOREM 122. If two polygons are similar, diagonals drawn from two corresponding vertices divide... | |
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FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
