 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...I. In any quadrilateral (not a parallelogram) 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 joining the middle points of the diagonals. COROLLARY II. In a parallelogram the sum of the squares... | |
 | George Albert Wentworth - 1889 - 264 pages
...of the diagonals (Ex. 19.) 23. 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. (Ex. 19.) * 24. The sum of the squares of the diagonals... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 204 pages
...median upon that side. 366. 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 joining the middle points of the diagonals. Sug. Use 365. What modification of the above theorem... | |
 | 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 times the square of the line joining the middle points of the diagonals. 5. Show that in a trapezoid, the sum of the squares... | |
 | 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 times the square of the line joining the middle points of the diagonals. '57 Hint. — Apply § 355, I. to the triangles ABC,... | |
 | 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 times the square of the line joining the middle points of the diagonals. 157 Hint.—Apply § 355, I. to the triangles ABC,... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...use similar triangles.] .Ex. 11. 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 midpoints of the diagonals. EXERCISES. CROUP 34 INDIRECT DEMONSTRATIONS Ex. 1. If... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...use similar triangles.] Ex. 11. 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 midpoints of the diagonals. EXERCISES. GROUP 34 INDIRECT DEMONSTRATIONS Ex. 1. If... | |
 | Joseph Claudel - Mathematics - 1906 - 758 pages
...base, and the diameter of the circle circumscribed about the triangle (673). 737. In any quadrilateral ABCD, 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 line which joins the middle points of the... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...fifth of the square ABCD. 945 The sum of the squares of the four sides of a 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. PLANE GEOMETRY — BOOK IV PROPOSITION XI. PROBLEM 423... | |
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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. 
