 | Robert Remington Goff - 1922 - 136 pages
...perimeters of two similar polygons are to each other as any two corresponding sides. *2g1. The perimeters of two regular polygons of the same number of sides are to each other as their radii and as their apothems. 292. What is a Constant, a Variable, a Limit? What is the usual... | |
 | David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...FUNDAMENTAL THEOREMS BOOK V Proposition 5. Perimeters of Regular Polygons 280. Theorem. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apothems. A' M' B Given two regular polygons of n sides, with centers... | |
 | National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...segment. 21. Parallelograms or triangles of equal bases and equal altitudes are equal. 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. Solid Geometry In the following list the precise wording and... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P:P'— OD : O'D' = AO:A'o'. QED 417. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 1315. The lines joining the mid-points of the radii of a regular... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...the polygon, the sum of the areas of the triangles is the area of the polygon. ... A = 437. Theorem. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, and also as the squares of their apothems. § 387 (2) EXERCISES 1. If r is... | |
 | Jacob William Albert Young - Mathematics - 1924 - 484 pages
...segment. 21. Parallelograms or triangles of equal bases and equal altitudes are equal. 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apot hems, Notes." I. The list I is typical, not exhaustive. 2. Concerning... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...Prop. V. Two regular polygons of the same number of sides are similar. 285. Prop. VII. The perimeters of two regular polygons of the same number of sides are to each other as their apothems or their radii. 284. Prop. VI. An equilateral polygon inscribed in a circle. 286. Prop.... | |
 | Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...perimeter by half its apothem. b. The area of a circle equals ?rr2 (informal proof only). 4. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. The treatment of the mensuration of the circle should be based on... | |
 | National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...Parallelograms or triangles of equal bases and equal altitudes are equal. [74, cd] 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. [83] * SOLID GEOMETRY In the following list the precise wording... | |
 | College Entrance Examination Board - Mathematics - 1920 - 108 pages
...question paper Mathematics CD, Plane and Solid Geometry, is printed on page 1.] 1. Prove: The perimeters of two regular polygons of the same number of sides are to each other as the radii or the apothems of the polygons. 2. Prove: In any circle the perpendicular to a radius at its... | |
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The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. 
