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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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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...perpendicular, each to each, the triangles are similar. 329. // two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. 342. In a right triangle, I. The altitude to 'he hypotenuse is a mean proportional between...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...SIMILAR POLYGONS' PROPOSITION XIX. THEOREM 329. If tico polygons are similar, they may be separated into the same number of triangles , similar, each to each, and similarly placed. ED E1 D' Given the similar polygons ABODE and A'B'C'D'E', divided into triangles by the diagonals...
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Plane Geometry Suggestive Method

George Clinton Shutts - 1905 - 260 pages
...demonstration. OD PROPOSITION XXIII. 309. Theorem. CONVERSE OF PROPOSITION XXII. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. GA G' A' Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...find the shortest side of the less. 327. THEOREM. If two polygons are similar, they may be decomposed into the same number of triangles similar each to each and similarly placed. Given : Similar polygons BE and B'E' ' . To Prove : A ABC similar to A A'B'C'; AACD similar...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 412 pages
...side of the less. PLANE GEOMETRY 327. THEOREM. If two polygons are similar, they may be decomposed into the same number of triangles similar each to each and similarly placed. Given : Similar polygons BE and B'E'. To Prove : A ABC similar to A A'B'C'; AACD similar to...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...similarly placed. IJ Given: ABCDEF and GHUKL, two similar polygons. To Prove : That the polygons can be divided into the same number of triangles, similar each to each and similarly placed. Proof : From the corresponding vertices A and G draw all diagonals possible. Then A CAB ~ A...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 206 pages
...manner, = = PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may lie decomposed into the same number of triangles, similar each to each, and similarly placed. 4 Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous ; and diagonals...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...(Why?) THEOREM XVII (Converse of Theorem XVI) 356. If two polygons are similar, they can be separated into the same number of triangles, similar each to each and similarly placed. Given : ABCDEF and GHIJKL, two similar polygons. To Prove : That the polygons can be divided...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...like manner, PROP. XIX. THEOREM 247. (Converse of Prop. XVIII.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. Z Draw similar polygons ABCDE, A'B'C'D'E', vertices E, E' being homologous; and diagonals...
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The Ohio Educational Monthly, Volume 58

Education - 1909
...equal to one-half of the third side. 2. Demonstrate: If two polygons are similar, they may be separated into the same number of triangles, similar each to each, and similarly placed. 3. Construct a fourth proportional to three given lines. 4. Demonstrate : Of isoperimetria...
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