| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 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... | |
| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...equal to angles A', B', C f , D\ E f respectively. To prove that ABCDE and A'B'C'D'E' can be separated **into the same number of triangles, similar each to each, and similarly** placed. Proof. Draw the corresponding diagonals DA, D ' A\ and DB > *>'*'* Since Z^=Z^ and DE : D'E'... | |
| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...ABC are similar. PROPOSITION XVIII. THEOREM 292. If two polygons are similar, they can Tie separated **into the same number of triangles, similar each to each, and similarly** placed. Given two similar polygons ABCDE and A'B'C'D'E' with angles A, B, C, D, E equal to angles A1,... | |
| John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 252 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,... | |
| 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... | |
| College Entrance Examination Board - Mathematics - 1915 - 60 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... | |
| John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 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... | |
| 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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