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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. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',... "
Elements of Geometry and Trigonometry: With Notes - Σελίδα 75
των Adrien Marie Legendre - 1828 - 316 σελίδες
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SOLID GEOMETRY

WILLIAM BETZ, HARRISON E. WEBB - 1916
...proportional between the whole hypotenuse and the adjacent segment. 412. If two polygons are similar, they are composed of the same number of triangles, similar each to each and similarly placed. 415. The perimeters of two similar polygons are to each other as any two homologous sides....

Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - 1916 - 467 σελίδες
...B AF + BD~ + CE = AE + BF2 + CD . " D PROPOSITION XV. THEOREM 293. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Hypothesis. AA EB ~ A A'E'B' ; A EBD ~ A .E'B'D' ; ABCD-AB'C'D'. The triangles are similarly...

Plane Geometry, with Problems and Application

Herbert Ellsworth Slaught - 1918 - 332 σελίδες
...perimeter of the larger. SIMILAR FIGURES TRIANGLES FORMING SIMILAR POLYGONS 362. THEOREM XV. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, then the polygons are similar. B' Given polygons P and P, composed of AI, II, III, and I',...

Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - 1918 - 310 σελίδες
...inches, find the perimeter of the larger. TRIANGLES FORMING SIMILAR POLYGONS 362. THEOREM XV. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, then the polygons are similar. B — — n B' Given polygons P and P, composed of AI, II, III,...

The Encyclopedia Americana: A Library of Universal Knowledge, Τόμος 25

1920
...similar. Two triangles which have their sides parallel or perpendicular, each to each, are similar. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. In solid geometry, similar polyhedrons are those whose corresponding...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1918 - 457 σελίδες
...similar. PROPOSITION XXV. THEOREM (303) (303) (Ax. 1.) (309) Q. E D. 314. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Given in the polygons ABCDE and A'B'C'D'E', AABE~ AA'B'E', ABCE ~ AB'C'E', A CDE ~ A C'D'E',...

Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 σελίδες
...AB AC BC DC AD DB (1) 13 12 (2) 12 i (3) 16 4 (4) 20 12 (5) 30 50 SIMILAR POLYGONS 441. Two polygons composed of the same number of triangles, similar each to each and similarly placed, are similar polygons. 442. Problem. Construct a polygon similar to a given polygon having given...

The Encyclopedia Americana: A Library of Universal Knowledge, Τόμος 25

1920
...similar. Two triangles which have their sides parallel or perpendicular, each to each, are similar. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. In solid geometry, similar polyhedrons are those whose corresponding...

School Education, Τόμος 17

1898
...a given point a parallel to a given straight line. 9. Show that two polygons are similar when they Are composed of the same number of triangles, similar each to each and similarly placed. 10. Show that two triangles having an angle of one equal to an angle of the other, are to each...

Solid Geometry

Charles Austin Hobbs - 1921 - 192 σελίδες
...triangles, similar each to each, and similarly placed. Prop. 88. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Prop. 90. The perimeters of two similar polygons are in the same ratio as any two homologous...




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