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" Similar triangles are to each other as the squares of their homologous sides. "
Elements of Geometry and Trigonometry: With Notes - Page 62
by Adrien Marie Legendre - 1822 - 367 pages
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Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 214 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. Bowdoin College, June, 1895. 1. The perpendiculars from the vertices of a triangle to the opposite...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...CE &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...
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Plane and Solid Geometry: Inductive Method

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...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...they 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,...
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Plane and Solid Geometry

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'...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...they 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...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...they 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...
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The Elements of Plane Geometry

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...
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Plane and Solid Geometry

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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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...A^.BC AABH AABC A DEF BC , 9 . /i// ^' vi/i • .BC />A' • EF B QED E PROPOSITION IX. THEOREM 616. Similar triangles are to each other as the squares of their homologous sides. B AAUC_AB • RC A DEF ~ DE.EF AB EF' BC ^ DE AABC IB* ADEF jjf? A Let To Prove Proof. C A^se and DEF...
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