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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, Τόμοι 6-9

George Albert Wentworth - 1899 - 218 σελίδες
...respectively parallel, or respectively perpendicular, are similar. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to...

The Essentials of Geometry

Webster Wells - 1899 - 395 σελίδες
...homologous base of a similar triangle is PROP. XX. THEOREM. 266. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. V Given, in polygons AC and A'C', A ABE similar to A A'B'E', ABCE to AB'C'E', and A CDE to...

The Essentials of Geometry

Webster Wells - 1899 - 395 σελίδες
...homologous base of a similar triangle is PROP. XX. THEOREM. 266. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Given, in polygons AC and A'C', A ABE similar to A A' B'E', A BCE to AB'C'E', and A CDE to...

Plane Geometry

William James Milne - 1899 - 242 σελίδες
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 309 SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ;...

Plane and Solid Geometry

William James Milne - 1899 - 384 σελίδες
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 301i SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10...

Plane and Solid Geometry

William James Milne - 1899 - 384 σελίδες
...PLANE GEOMETRY. — BOOK IV. Proposition XII 309. Draw two polygons such that they may be divided into the same number of triangles, similar, each to each, and similarly situated. How do the homologous angles of these polygons compare in size? How do the ratios of any two pairs...

Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - 1901 - 266 σελίδες
...similar manner we may prove that A AED is similar to A FKI. Therefore, etc. Con. — CONVERSELY : If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the two polygons are similar. This may be readily proved, the demonstration being almost the...

Elements of Plane Geometry

Alan Sanders - 1901 - 247 σελίδες
...circles. Draw the two common chords. PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and .similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and...

Plane Geometry

Arthur Schultze - 1901
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. ED Hyp, In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', D A CDE ~...

Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 σελίδες
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. E' D' ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE...




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