 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...AEF are similar. PROPOSITION XVIII. THEOREM 292. If two polygons are similar, they can be separated into the same number of triangles, similar each to each, and similarly placed. A3 A' B' Given two similar polygons ABCDEand A'B'C'D'E' with angles A, B, C, D, E equal to... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...165. Definitions. Similar Polygons. Two polygons are said to be similar when each in ay be decomposed into the same number of triangles similar each to each and similarly placed. Thus, in the figure, the polygons ABCDE and A'B'C'D'E' are similar. For, if we draw the lines... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...Given the similar polygons ABCDE • • • and A'B'C'D'E' •••. To prove that the polygons can be divided into the same number of triangles, similar each to each, and similarly placed. Proof. 1. Join any point 0 in ABCDE ••• to the vertices A, B, C, —. Construct A B'A'O'... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 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'... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 296 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,... | |
 | College Entrance Examination Board - Mathematics - 1915 - 72 pages
...projection of the longest side upon the shortest side. 6. If two polygons are similar, they can be separated into the same number of triangles, similar each to each, and similarly placed. GROUP B. (Answer two questions from this group.) 7. A circle, radius 5 inches, contains a moving... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...the larger polygon. PROPOSITION XXX. THEOREM 318. If two polygons are similar, they may be decomposed into the same number of triangles, similar each to each and similarly placed. B' B EDE D' Given: Similar polygons BE and B'E'. To Prove : A ABC similar to A A'B'C' ; A ACD... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...angle of elevation of the sun ? PLANE GEOMETRY 425. THEOREM. Two similar polygons can be decomposed into the same number of triangles, similar each to each, and similarly placed. Fio. 196. Given the similar polygons ABCDE •.. and A'B'O'D'E' —. To prove that the polygons... | |
 | 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'... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...CD + etc. MN+ NO+OP + etc. MN Def. sim. poly. § H8, (8) 137. Theorem. — Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. D Hypothesis. AB CD • • • and MNOP • • • are similar polygons. 122 Suggestions.... | |
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Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
