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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.
A Text-book of Geometry - Page 211
by George Albert Wentworth - 1888 - 386 pages

Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...*2Q0. The 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...

General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...equal. . 4. This is obvious from 3. 5. By definition of similar polygons. 534. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. 535. Theorem. The perimeter of two regular polygons of the same number of sides...

General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...equal. 4. This is obvious from 3. 5. By definition of similar polygons. 420 535. Theorem. The perimeter of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Given the regular polygons AB • • • and A'B • • • of...

Plane Geometry: Experiment, Classification, Discovery, Application ...

Clarence Addison Willis - Geometry, Modern - 1922 - 320 pages
...of a regular hexagon whose apothem is 34.64? THE SECOND STEP IN CLASSIFICATION 336. Theorem I. — The perimeters of two regular polygons of the same number of sides are proportional to the radii of the polygons. Hypothesis. — Regular polygons 0 and 0', of the same number...

Plane Geometry: Experiment, Classification, Discovery, Application ...

Clarence Addison Willis - Geometry, Modern - 1922 - 318 pages
...a regular hexagon whose apothem is 34.64? THE SECOND STEP IN CLASSIFICATION 336. Theorem I.-—The perimeters of two regular polygons of the same number of sides are proportional to the radii of the polygons. Hypothesis.—Regular polygons 0 and 0', of the same number...

Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...corresponding sides. 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...

The Reorganization of Mathematics in Secondary Education: A Report of the ...

National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...external 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...

Schultze and Sevenoak's Plane and Solid Geometry

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...