 An equiangular polygon inscribed in a circle is regular if the number of its sides is odd. PROPOSITION VIII. THEOREM 405. Regular polygons of the same number of sides are similar. E Hyp. ABCDE and A'B'C'D'E' are regular polygons of n sides.  Plane and Solid Geometry - Page 299by Webster Wells, Walter Wilson Hart - 1916 - 467 pagesFull view - About this book
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...equilateral polygon circumscribed about a circle is regular if the number of its sides is odd. 2. Every equiangular polygon inscribed in a circle is regular if the number of its sides is odd. 3. The area of the inscribed regular dodecagon is equal to three times the square... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...sum of the two cres- ~ ' cents AcBa and BdCb equals the area of the right triangle ABC. .3 C? Ex. 31. An equiangular polygon inscribed in a circle is regular if the number of its sides be odd. [Sue. In the figure to Prop. Ill, p. 264, arc AEDC=-&ic EDCB ,'. are AE=&ro BC, :.... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...that the sum of the two crescents AcBa and BdCb equals the area of the right triangle ABC. Ex. 31. An equiangular polygon inscribed in a circle is regular if the number of its sides be odd. [SuG. In the figure to Prop. Ill, p. 264, arc AEDC^wc EDCB /. are AE—&TQ BC, .'.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...(THEOREMS) 1. The central angle of a regular polygon is the supplement of the angle of the polygon. 2. An equiangular polygon inscribed in a circle is regular (if the number of its sides is odd). 3. An equiangular polygon circumscribed about a circle is regular. [Draw radii and... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(THEOREMS) 1. The central angle of a regular polygon is the supplement of the angle of the polygon. 2. An equiangular polygon inscribed in a circle is regular (if the number of its sides is odd). 3. An equiangular polygon circumscribed about a circle is regular. [Draw radii and... | |
 | Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...areas ? BOOK V. REGULAR POLYGONS. MEASUREMENT OF THE CIRCLE Group I. Regular Polygons. Theorems 1 . An equiangular polygon inscribed in a circle is regular if the number of sides is odd. 2. An angle at the center of a regular polygon is equal to four right angles divided by the number... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...16 and 30; find the area of the circle inscribed in the rhombus. MISCELLANEOUS EXERCISES Ex. 1026. An equiangular polygon inscribed in a circle Is regular if the number of sides is odd. Ex. 1027. An equilateral polygon circumscribed about a circle is regular if the number of sides is odd.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...quadrilateral is equal to the sum of the products of the opposite sides. (Ptolemy's Theorem.) Ex. 1389. An equiangular polygon inscribed in a circle is regular if the number of sides is odd. Ex. 1390. If circles be circumscribed about the four triangles into which a quadrilateral is divided by... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...quadrilateral is equal to the sum of the products of the opposite sides. (Ptolemy's Theorem.) Ex. 1389. An equiangular polygon inscribed in a circle is regular if the number of sides is odd. Ex. 1390. If circles be circumscribed about the four triangles into wliicli a quadrilateral is divided... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...figure for § 365 prove that : (a) S4>ss>si6, etc. (See §362.) (6) a4<as<ai6, etc. (c) *4 < &s < fo6, etc. Ex. 5. Prove that an equiangular polygon inscribed...equiangular; (c) that XY = YZ, etc. See diagram in § 307. Complete the proof. Ex. 7. Repeat Ex. 14, p. 227, for a regular octagon circumscribed about... | |
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