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" The areas of two similar triangles are to each other as the squares of any two homologous sides. "
Plane Geometry - Page 190
by Arthur Schultze - 1901
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...quan• tity ^p, and reducing, we have ACD : PQR :: CD2 : QR2. But, CD2:QR2::DA2:RP2::AC2:PQ2. c Hence, two similar triangles are to each other as the squares of any two homologous sides. Cor. 2. If ACD and PQR are similar, ACD and EFD are also similar; consequently the second couplets...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...similar triangles, homologous altitudes are to each other as any pair of homologous sides. XXVI. Theorem. The areas of two similar triangles are to each other as the squares of two homologous sides or altitudes. abc. ABC : abc = HYPOTH. A ABC ~ To IJE PROVED. AB2 : a&2. PROOF....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...triangles ABC and DEF be similar, the angle A being equal to the angle D, B to E, and C to F : then the triangles are to each other as the squares of any two homologous sides. Because the angles A and D are equal, we have (P. XXTV.), ABC : DEF : : ABxAC : DE x DF ; and,...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...hence, CD AB C'D' A'B' Substituting in (1), we have ABC = A'B'C' A'B AB AB A'B' AB2 335. SCHOLIUM. Two similar triangles are to each other as the squares of any two homologous lines. PROPOSITION VIII. THEOREM. 336. Two triangles having an angle of one equal to an angle of the...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...equalities, AABC_ABxAC AADE ADxAE 370 q. ED COMPARISON OF POLYGONS. PROPOSITION VIII. THEOREM. 375. The areas of two similar triangles are to each other as the squares of any two homologous sides. Let the two triangles be ACS and A'CB'. A ACB AJ? Draw the perpendiculars CO and C'O'. A ACB...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...equal ^57^ . D .A. r> O A ABC BC BC BC' ' ' ' A A'B'C' ~ B'C' X B'C' - g^c'' • Q•KD• 378. Cor. The areas of two similar triangles are to each other as the squares of any two homologous lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...in the above equality for -=^-, its equal T^^-, A ABC BC BC _ BC' A A'B'C' " B'C' 378. Cor. The arms of two similar triangles are to each other as the squares of any two homologous lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1891 - 424 pages
...A ABC BC BC EC ' 1 ' A A'B'C 7 " B'C' B'C' ~~ B/C"' ' ' '• 7 " '' X _ 378. Cor. The areas of (wo similar triangles are to each other as the squares of any two homologous lines. EXERCISES. 1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1894 - 456 pages
...PLANE GEOMETRY. — BOOK IV. COMPARISON OF POLYGONS. PROPOSITION VIII. THEOREM. 375. The areas of tivo similar triangles are to each other as the squares of any two homologous sides. A 0 B A! O' B' Let the two triangles be ACB and A'GB'. A ACB Al? To prove A A'C'B' Draw the...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...formed by a straight line parallel to the base, and distant 5 feet from the vertex ? 2. Prove that the areas of two similar triangles are to each other as the squares of the radii of their inscribed circles. 3. Prove that the area of a circumscribed polygon is equal...
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