 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...rectangles on the including sides. 4. Show that the sum of the squares of the sides of any quadrangle equals the sum of the squares of the diagonals plus four...the line joining the middle points of the diagonals. 5. Show that in a trapezoid, the sum of the squares of the diagonals equals the sum of the squares... | |
 | John Casey - Geometry - 1895 - 216 pages
...The sum of the squares of the four sides of a quadrilateral is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals. ~~~~~^-o Dem.— Let ABCD be the quadrilateral, E, F the middle points of the diagonals. Now, in the... | |
 | Elias Loomis - Geometry - 1895 - 450 pages
...PROPOSITION VJLU. 12. In any quadrilateral, the sum of the squares of the four sides is equal to the gum of the squares of the diagonals plus four times the square of the line which joins the middle points of the diagonals. Let ABCD be any quadrilateral, and let E and F be the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...325, 326. 356. Exercise. — In any quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four...the line joining the middle points of the diagonals. '57 Hint. — Apply § 355, I. to the triangles ABC, ADC, and BED, and combine equations thus obtained.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...325. 326. 350. Exercise. — In any quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four...the line joining the middle points of the diagonals. 157 Hint.—Apply § 355, I. to the triangles ABC, ADC. and BED, and combine equations thus obtained.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...of the squares of the four sides of a quadrilateral is equivalent to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals. Appl. Prove AI? + B(f + Cff + DA* = AC* + BD* + 4 EF~ Cons. Draw BF and DF Dem. AB * +BC * = 2AF *... | |
 | George Albert Wentworth - Geometry - 1896 - 296 pages
...the four sides of any quadrilateral is. equal to the sum of the squares of the diagonals increased by four times the square of the line joining the middle points of the diagonals. Let ABCD be a quadrilateral, and EF the line joining the middle points of the diagonals AC and BD.... | |
 | Frederick Harold Bailey - Geometry, Analytic - 1897 - 392 pages
...sides of any quadrilateral is equivalent to the sum of the squares on the diagonals, together with four times the square of the line joining the middle points of the diagonals. / .' .•-.. ,". -\^-» ! . . X ,,i' > ; • - '• " . A V " " • . . i, . .' CHAPTER II. LOCL 11.... | |
 | George Albert Wentworth - Geometry - 1898 - 266 pages
...of any quadrilateral is equal to the sum of the squares of the diagonals, increased by four -iimes the square of the line joining the middle points of the diagonals. HINT. Join the middle points F, E, of the diagonals. Draw EB and ED. Apply \ 344 to the A ABC and ADC,... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...sum of the squares of the four sides is equal to the sum of the squares of the diagonals increased by four times the square of the line joining the middle points of the diagonals. HINT. Draw AF and CF, and use the same method of proof as in Prop. 154. Ex. 441. Two circles intersect... | |
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The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals. 
