 The homologous sides of similar triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides.  A Treatise on Special Or Elementary Geometry - Page 60by Edward Olney - 1872 - 239 pagesFull view - About this book
 | 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'... | |
 | Arthur Schultze - 1901 - 260 pages
...the ratio of A ABC to Ex. 826. If A ABC~&A'B'C', and /LA = Z 4', then PROPOSITION XVI. THEOREM 370. Similar triangles are to each other as the squares of their homologous sides. Hyp. A To prove Proof. c A' AABC~AA'B'C'. A ABC AT? A ABC = A A'B'C' A'B' x A'C ' A'B' " .4'C"" ^'5'... | |
 | Arthur Schultze - 1901 - 392 pages
...AA'B'C'. Ex. 826. If A ABC~AA'B'C', &ndZA = 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. QED Ex. 827. The sides of a triangle are 4, 7, and 8. What are the sides of a similar triangle, whose... | |
 | 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... | |
 | 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.... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...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 - 1901 - 394 pages
...parallelograms are to each other as the products of their diagonals. 373. REMARK. As similar polygons (and triangles) are to each other as the squares of their homologous sides, Prop. XI may be used to draw a polygon that shall be any given part of a given polygon, and similar... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...ABC _ AB . BC j?x &DEF~ DE . EF AB_ _ B£ ,„ DE EF A ABC AB2 ,„. A^ = ^' (?) QE'D617. EXERCISE. Similar triangles are to each other as the squares of their homologous altitudes. 618. EXERCISE. In the triangle ABC, ED is parallel to AC, and CD = J DB. How do the areas... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...Ex. 826. If A ABC- A A'B'C", and ZA = Z .4', then AB:A'S' = A'C' :AC. PROPOSITION XVI. THEOREM . 370. Similar triangles are to each other as the squares of their homologous sidex. Hyp. To prove Proof. A ABC A ABC AT? AA'B'O AB x AC AB x AC AA'B'C' A'B' x A'C' A'B' "A'C .... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...DE is 12 ft. How long is EF? AABC A ABH BC_ BH (?) AABC Ajt • BC QED PROPOSITION IX. THEOREM 616. Similar triangles are to each other as the squares of their homologous sides. Let To Prove Proof. A ABC and DEF be similar. AABC_ AB2 A DEF JJx* ZB = Zi'. (?) A ABC AB.BC ,„.... | |
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