 | Maxime Bôcher - Geometry, Analytic - 1915 - 260 pages
...sides are equal.] 6. Prove that 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 distance between the middle points of the diagonals. 7. Prove that if the lines joining two vertices... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...D'i If £ falls on D'! 31. 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 times ^ the square of the line-segment joining the middle points of the diagonals. SUGGESTION. — ED, EB, and EF are medians... | |
 | John Wesley Young, Frank Millett Morgan - Functions - 1917 - 586 pages
...the third side. 12. Prove that 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 distance between the middle points of the diagonals. 13. If A, B, C, D are four points of a line prove... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...harmonically. (301, 302.) * Ex. 1076. The sum of the squares of the four 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 mid-points of the diagonals. (337.) * Ex. 1077. If from a point within the triangle... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...of opposite sides are equal. 2. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals plus four times the square on the line connecting their middle points. Suggestion. AE, CE, EF are medians of A ABD, BCD, and CEA,... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...of opposite sides are equal. 2. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals plus four times the square on the line connecting their middle points. Suggestion. AE, CE, EF are medians of & ABD, BCD, and CEA,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...harmonically. (301, 302.) * Ex. 1076. The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the Hue joining the mid-points of the diagonals. (337.) * Ex. 1077. If from a point within the triangle... | |
 | Alain Robert - Mathematics - 2005 - 390 pages
...identities - = ||x||2 + 2(xy) + ||y||2, (1) If we add them, we find This is the parallelogram equality: The sum of the squares of the sides is equal to the sum of the squares of the diagonals. x + y xy shows that the sum ||x||2 + ||y||2 is the mean value of the squares... | |
 | Claudi Alsina, Roger B. Nelsen - Education - 2006 - 202 pages
...quadrilaterals. Theorem. In any convex quadrilateral the sum of the squares of the sides is equal to the sum of the squares of the diagonals plus four times the square of the distance between the midpoints of the diagonals. See Figure 20.4. = e2 +f2 + 4g2 FIGURE 20.4 Proof.... | |
 | Actuarial Society of America - Insurance - 1915 - 478 pages
...tangent to a given circle and passing through a given point. 7. Prove that in any quadrilateral the sum of the squares of the 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... | |
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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. 
