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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. "
New Elementary Geometry: With Practical Applications : a Shorter Course Upon ... - Page 88
by Benjamin Greenleaf - 1874 - 176 pages
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Plane and Solid Geometry

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...
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Plane and Solid Geometry

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'...
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Plane and Solid Geometry

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,...
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Plane Geometry

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'...
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Plane Geometry

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'...
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Plane Geometry

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,...
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Robbin's New Plane Geometry

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...
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Examination Questions in Mathematics: Third Series, 1911-1915

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...
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Plane Geometry

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...
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Plane Geometry

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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