 | Geometry, Plane - 1911 - 192 pages
...that the theorem has been proved for commensurable parts, prove it for incommensurable parts. 6. Two similar triangles are to each other as the squares of their homologous sides. 6. To draw a line parallel to the base of a triangle dividing its area into two equivalent parts. 7.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...and ZA = ZA'. Find AC if AB = 2 in., 4'J3' = 3 in., and 4'C' = 4 in. PROPOSITION XIV. THEOREM 379. Similar triangles are to each other as the squares of their homologous sides. Given To prove Proof. A ABC ~ AA'B'C A ABC ~AB L AA'B'C' ZA A ABC AB X AC AA'B'C' ''A'B'xA'C" (303)... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...are to each other as the products of their diagonals. 381. METHOD XXI. As similar polygons (including triangles) are to each other as the squares of their homologous sides, Prop. IX may be used to draw a polygon that shall be any given part of a given polygon, and similar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...are to each other as the products of their diagonals. 381. METHOD XXI. As similar polygons (including triangles) are to each other as the squares of their homologous sides, Prop. IX may be used to draw a polygon that shall be any given part of a given polygon, and similar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...Ex. 1158. If A ABC = A A'B'C', and £A = £ A', then AB:A'B' =A'C' :AC. PROPOSITION XIV. THEOREM 379. Similar triangles are to each other as the squares of their homologous sides. "AA'B'C' A'B'XA'C'' AB ., AC C', (303) (378) AB AB In like manner A'B' A ABC ACT AA'B'C' QED Ex. 1159.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...in., and A'C' = 4 in. ^'C' B'D ^C ^ AB : A'C' A'B" AC X AB 'A'C' x A'B'' PROPOSITION XIV. THEOREM 379. Similar triangles are to each other as the squares of their homologous sides. fGiven A ABC ~ &A'B'C A ABC ~ABZ HC2 SO2 _ To prove AA'B'C' A'Bft A'Cft We* Proof. ^A=ZA'. (303) A... | |
 | University of the South - 1906 - 204 pages
...angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 5. Two similar triangles are to each other as the squares of their homologous sides. 6. The area of a circle is equal to one-half the product of its circumference and radius. AMERICAN... | |
 | Mathematics - 1904 - 1000 pages
...proposition is not at all clear to some students until interpreted by numerical exercises. The sentence, "Similar triangles are to each other as the squares of their homologous sides," and the corresponding algebraic symbols, should be made perfectly clear by numerical applications,... | |
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Similar triangles are to each other as the squares of their homologous sides. 
