Mathematics
In the adjoining figure, D and E are mid-points of the sides BC and CA respectively of a △ABC, right angled at C. Prove that :
(i) 4AD2 = 4AC2 + BC2
(ii) 4BE2 = 4BC2 + AC2
(iii) 4(AD2 + BE2) = 5AB2
Related Questions
If AD, BE and CF are medians of △ABC, prove that
3(AB2 + BC2 + CA2) = 4(AD2 + BE2 + CF2).
AD is perpendicular to the side BC of an equilateral △ABC. Prove that 4AD2 = 3AB2.
In the figure given below, ABCD is a square of side 7 cm. If
AE = FC = CG = HA = 3 cm,
(i) prove that EFGH is a rectangle.
(ii) find the area and perimeter of EFGH.
In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O, at right angles. Prove that AB2 + CD2 = AD2 + BC2.
