JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Properties of Some Geometrical Figures

(1) In a triangle ABC, if AD is the median drawn to BC, then \[A{{B}^{2}}+A{{C}^{2}}=2(A{{D}^{2}}+B{{D}^{2}})\]

(2) A triangle is isosceles if any two of its medians are equal or two sides are equal.

(3) In a right angled triangle, the mid-point of the hypotenuse is equidistant from the vertices.

(4) Equilateral triangle : All sides are equal.

(5) Rhombus : All sides are equal and no angle is right angle, but diagonals are at right angles and unequal.

(6) Square : All sides are equal and each angle is right angle. The diagonals bisect each other.

(7) Parallelogram : Opposite sides are parallel and equal and diagonals bisect each other.

(8) Rectangle : Opposite sides are equal and each angle is right angle. Diagonals are equal.

(9) The figure obtained by joining the middle points of a quadrilateral in order is a parallelogram.