 | Joe Garner Estill - 1896 - 186 pages
...employed. (b) Find the area of the regular circumscribed hexagon of a circle whose radius is 1. 6. Two similar triangles are to each other as the squares of their homologous sides. Bowdoin College, June, 1895. 1. The perpendiculars from the vertices of a triangle to the opposite... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...&ABE &ADE AABE BE (C y DE § 232, 3. AE X BE ' A CDE CE X DE PROPOSITION XXV. THEOREM. QED 2G9. Two similar triangles are to each other as the squares of their homologous sides. c A? B N Given —AC and DF, homologous sides of the similar triangles ABC and DEF. To Prove— A ABC... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...intercept, the areas of the figures may be found by §§ 312 and 316. PROP. VII. THEOREM. 319. Two similar triangles are to each other as the squares of their homologous sides. O •"• D '•> Given AB and A'B' homologous sides of similar A ABC and A'B'C', respectively. 314,... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...employed. (6) Find the area of the regular circumscribed hexagon of a circle whose radius is 1. 6. Two similar triangles are to each other as the squares of their homologous sides. BOOK VI. SOLID GEOMETRY, PRELIMINARY DISCUSSION. 378.' 1. (1) Construct three plane figures; two not... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...intercept, the areas of the figures may be found by §§ 312 and 316. PROP. VII. THEOREM. 319. Two similar triangles are to each other as the squares of their homologous sides. C AD " Given AB and A'B' homologous sides of similar &ABC and A'B'C', respectively. ABC AS To Prove... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...angle of the other, the sides about the third angles are proportional. Proposition 177. Theorem. 213. Similar triangles are to each other as the squares of their homologous sides. Consult Prop. 166, Cor. V. and Prop. 140. Proposition 178. Theorem. 214. Similar polygons are to each... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...Multiplying these ratios (by 207), ABC x ABE = ACxAB ABE x ADE ~ AEx AD' PROPOSITION VIII. THEOREM. 262. Two similar triangles are to each other as the squares of their homologous sides. C Let AB and A'B' be homologous sides of the similar triangles ABC and A'B'C'. To prove that A'B'C'... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...intercept, the areas of the figures may be found by §§ 312 and 316. PROP. VII. THEOREM. 319. Two -similar triangles are to each other as the squares of their homologous sides. C D B Given AB and A'B' homologous sides of similar A ABO and A'B' C", respectively. ABC AT? To Prove... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...GHC = AC x BC : GC x HC. Or, A ABC: &DEF=ACx BC : DF x EF. Therefore, etc. PROPOSITION XXVIII. — THEOREM. Similar triangles are to each other as the squares of their homologous sides. Given. — Let ABC and DEF be similar triangles, having the angle A equal to the angle D, the angle... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...to Ex. 826. If A ABC~AA'B'C', andZA = Z A', then AB:A'B' = A'C(: AC. PROPOSITION XVI. THEOREM 370. Similar triangles are to each other as the squares of their homologous sides. AJt J~» Proof. A ABC = ABxAC = AB AC = AB AB AB? A A'B'O A'B' x AC' AB' A'C' A'B' A'B'~ QED Ex. 827.... | |
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Similar triangles are to each other as the squares of their homologous sides. 
