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" The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. "
An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in ... - Page 117
by Francis Joseph Grund - 1834 - 190 pages
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...perimeters are in the same ratio as the apothems. The same holds true for the radii. 352. COROLLARY III. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of their radii, or as the squares of their apothems. (Art. 315.) EXERCISES 1. Tangents to a...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...as the radii of the polygons, or as the apothems of the polygons. 351. COROLLARY II. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii, or as their apothems. Let Si and ,Sa be the lengths of the sides in two regular polygons...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...= OA: O'A' = OM : O'M'. 445 364 431 436 Also, . 357 351 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles....
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Catalogue ...

Yale University. Sheffield Scientific School - 1905 - 1074 pages
...square and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons' of the same number of sides are in the same ratio as the radii of the inscribed or circumseribed circles. 5. To construct a circle of a given radius tangent...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...number of sides are in the same ratio as their radii, or as their apothems. 434. The areas of regular polygons of the same number of sides are in the same ratio as the squares of their radii, or as the squares of their apothems. 435. The area of a regular polygon is...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...( 64, Axiom 5) (Why?) GH HI .'. the polygons are similar. 432. Corollary. The perimeters of regular polygons of the same number of sides are in the same ratio as any two corresponding sides. THEOREM IV 433. The perimeters of regular polygons of the same number...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...} '"' A'B' +B'C' + C'D' + -~ A1B' r'~a'' Draw the figure and give the proof in full. 348. THEOREM. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the corresponding radii or apothems. Outline of Proof : Divide the polygons into pairs of...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...A'B' +B'C' + C' D' + ••• A'B' r' a' Draw the figure and give the proof in full. 348. THEOREM. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the corresponding radii or apothems. Outline of Proof : Divide the polygons into pairs of...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...corresponding angles equal. Therefore the two polygons are similar, by 282. QED 374. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...drawn from the point of tangency, prove that they are divided proportionally by the smaller circle. 6. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or their apothems. 6. Prove that if one acute angle of...
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