 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...A A'B'C' + A A'C'D" ' ' A A'B'C' . P R ~ A .4'£' C" ~~ JAB'2' 0. ED 437. COB. 1. T%e areas of two similar polygons are to each other as the squares of any two homologous lines. 438. COR. 2. Two homologous lines of two similar polygons are to each other as the square roots... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...£=£. (Why?) See §128. Therefore -•-. QED FIG. 277 Areas of Polygons PROPOSITION IX 247. Theorem: The areas of similar polygons are to each other as the squares of the homologous sides. Hypothesis: Polygon ABC .... ^polygon A'B'C'. . . . (Fig. 278). Let P denote... | |
 | Geometry, Plane - 1911 - 192 pages
...triangles whose sides are respectively perpendicular to each other are similar. 3. The areas of two similar polygons are to each other as the squares of any two homologous sides. 4. Construct a regular octagon having given one side. 6. If in any triangle a medium be drawn from... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...503. 5. § 503. 6. § 419. 7. § 54,13. 8. § 54,1. -A 111' a 2 a. Q ' E - D 10 § 309. 506. Cor. Two similar polygons are to each other as the squares of any two homologous diagonals. Ex. 879. If one square is double another, what is the ratio of their sides ? Ex. 880. Divide... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...length of the homologous altitude of the other triangle ? PROPOSITION XIX. THEOREM 416. The areas of two similar polygons are to each other as the squares of any two homologous sides. Given the two similar polygons Pand P',with the areas S and S' and the homologous sides a and a'. To... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...other, are to each other as the products of the sides including the equal angles. 436. The areas of two similar polygons are to each other as the squares of any two homologous sides. 486. If the number of sides of an inscribed polygon be indefinitely increased, the apothem of the polygon... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...§ 503. 4. § 503. 5. § 503. 6. §419. 7. § 54, 13. 8. §54,1. 9. §401. 10 § 309. 506. Cor. Two similar polygons are to each other as the squares of any two homologous diagonal?. Er. 879. If one square is double another, what is the ratio of their sides ? Hx. 880. Divide... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...are to each other as the squares of any two corresponding sides. 195. Corollary 1. The areas of two similar polygons are to each other as the squares of any two corresponding sides. The areas of two similar polygons are to each other as the squares of any two... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...two similar figures are proportional to two corresponding sides, it follows that the areas of any two similar polygons are to each other as the squares of any two corresponding lines. Compare, in particular, Exs. 4 and 6, p. 171. EXERCISES 1. Compare the areas of... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...A'C' A'B' A ABC AB . AB Why? § 193 Why? AA'B'C' A'B'- A'B' A'B'* 195. Corollary 1. The areas of two similar polygons are, to each other as the squares of any two corresponding sides. [HINT Divide the polygons up into the same number of similar triangles, as in... | |
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The areas of two similar polygons are to each other as the squares of any two homologous sides. 
