 | John Casey - Geometry - 1888 - 279 pages
...+4FB2 = AC2 +BD2 + 4EE2. Prop. 5. — Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the lines bisecting the sides of the triangle. Dem. — Let D, E, F be the middle points of the sides. Then AB2... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...the quadrilateral. 4. Prove that five times the square of the hypotenuse of a right-angled triangle is equal to four times the sum of the squares of the medians from its extremities. PROPOSITION XXIII. 416. Theorem : Of three similar figures constructed... | |
 | Seth Thayer Stewart - Geometry - 1893 - 262 pages
...alternate Zs; ie, EO = OF. 4. Prove that five times the square of the hypotenuse of a right-angled triangle is equal to four times the sum of the squares of the medians from its extremities. Let A, B, C, be the three sides of at^, A being the hypotenuse ; and... | |
 | Arthur Schultze - 1901 - 392 pages
...a diameter bisects the base. Ex. 740. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. Ex. 741. If in the parallelogram ABCD ZA = 00°, AC* = AB* + BC* + AB x. BC. Ex. 742. If the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...a diameter bisects the base. Ex. 740. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. Ex. 741. If in the parallelogram ABCD ZA = 60°, AC'2 = AB2 + BC2 + AB x BC. Ex. 742. If the... | |
 | Arthur Schultze - 1901 - 260 pages
...a diameter bisects the base. Ex. 740. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. Ex. 741. If in the parallelogram ABCD ZA = 00°, AC2 = AB2 + BC2 + ABx BC. Ex. 742. If the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...a diameter bisects the base. Ex. 740. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. Ex. 741. If in the parallelogram ABCD ZA = 60°, A~C2 = AB2 + BC2 + AB x BC. Ex. 742. If the... | |
 | Clement Vavasor Durell - Geometry, Plane - 1909 - 244 pages
...that a = */2 (b** c). 49. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. 50. If ABCD is a parallelogram, prove that 51. P, Q are the mid-points of the diagonals AC,... | |
 | Clement Vavasor Durell - Geometry, Plane - 1909 - 244 pages
...prove that <z = s/2 (b~c). 49. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. 50. If ABCD is a parallelogram, prove that 51. P, Q are the mid-points of the diagonals AC,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...adjacent sides are proportional. Ex. 1069. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. Ex. 1070. If in rectangle ABCD a perpendicular is drawn from D upon AC, the prolongation of... | |
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Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. 
