| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...Theorem VIII. Two regular polygons of the same number of sides are similar. Corollary 1. The perimeters **of regular polygons of the same number of sides are to each other as** their apothems, as their radii, to their sides. Corollary 2. The areas of regular polygons are to each... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...Theorem VIII. Two regular polygons of the same number of sides are similar. Corollary 1. The perimeters **of regular polygons of the same number of sides are to each other as** their apothems, as their radii, to their sides. Corollary Z. The areas of regular polygons are to each... | |
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...= etc. Ax. V MN NO 9. .-. ABCD MNOP -. Def. sim. poly. 252. Corollary. — The areas of two regular **polygons of the same number of sides are to each other as the squares** of their sides. 253. Theorem. — The perimeters of two regular polygons of the same number of sides... | |
| William Betz - Geometry - 1916 - 536 pages
...circle into two arcs having the ratio 1:8 (1:5, 2:3, 3 : 7, 7 : 8). 454. The perimeters of two regular **polygons of the same number of sides are to each other as** their radii and also as their apothems. Given two regular polygons, each having n sides, and with the... | |
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...squares of their sides. The proof is left to the student. 253. Theorem. — The perimeters of two regular **polygons of the same number of sides are to each other as** their radii, or as their apothems. Hypothesis. AB and CD are sides, and M and N the centers, respectively,... | |
| Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...the circumscribed equilateral triangle is 1 to 4. 256 PROPOSITION VII. THEOREM 377. The perimeters **of regular polygons of the same number of sides are to each other as the** radii of the circumscribed circles, or as the radii of the inscribed circles. Given AC and A' C' two... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...AO : A'o'. (303) But P:P' = AB:A'B' = AD:A'D'. (Why?) ...P:P' = OD:O'D' = AO:A'0'. 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 pentagon... | |
| Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...equal to half the product of the perimeter by the apothem. § 479. 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. . MEASUREMENT OF THE CIRCLE § 485. Theorems... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...areas of the triangles is the area of the polygon, .-. A - %ap. 479. 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. EXERCISES 1. Prove that the area of a regular... | |
| United States. Office of Education - 1921 - 1286 pages
...Parallelograms or triangles of equal bases and 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 apothème. SOL[D GEOMETRY. In the following list the precise wording... | |
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