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" If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. "
Plane Geometry - Page 170
by Webster Wells, Walter Wilson Hart - 1915 - 309 pages
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...homologous angles, vertices, sides, and diagonals. 154. Theorem. Two similar polygons are divisible into the same number of triangles, similar each to each, and similarly placed. 155. Theorem. Two polygons are similar if they are divisible into the same number of triangles, similar...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...each to each, and . similarly placed. 155. Theorem. Two polygons are similar if they are divisible into the same number of triangles, similar each to each, and similarly placed. 156. Theorem. The perimeters of two similar polygons are proportional to any two homologous sides....
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...are parallel or perpendicular are similar. Proposition V. A Theorem. 210. Two similar polygons may be divided into the same number of triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar...
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...are parallel or perpendicular are similar. Proposition V. A Theorem. 210. Two similar polygons may be divided into the same number of triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...hoinohgous sides PLANE GEOMETRY. Proposition 22. Theorem. 321. Conversely, two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. . Hyp. Let AB0DE, A'B'C'D'E' be two similar polygons divided into AS by the diagonals AC, AD, A'C',...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...and DE = 5, find B'D', D'E', and AE'. Proposition 21 . Theorem. 320. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. Hyp. Let the As ABC, ACD, ADE of the polygon ABCDE be similar respectively...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...Conclusion : AB 0 and GHJ being any similar, etc. PROPOSITION XIII. 4O4. Theorem : Polygons composed of the same number of triangles, similar each to each, and similarly placed, are similar. Statement: Let any polygons, ABK and FSI, contain the same number of triangles, /, 2,...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same number of triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...Complete the demonstration. PROPOSITION XXIII. 309. Theorem. CONVERSE or PROPOSITION XXII. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. GA Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be drawn from...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...escribed, and circumscribed circles of any triangle. 3. (a) Two polygons are similar when composed of the same number of triangles, similar each to each, and similarly placed. 4. In the triangle whose sides are a, b, and c, determine the segments of each side made by the bisector...
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