Prove that a cyclic rhombus is a square

Prove that the area of a rhombus is equal to half of the product of the diagonals.

What is a cyclic process ?

State whether the statements are True or False. (v) Every rhombus is a square ( )

State the reasons for the following. (i) A square is a special kind of a rectangle. (ii) A rhombus is a special kind of a parallelogram. (iii) A rhombus and a kite have one common property. (iv) A square and a rhombus have one common property.

Prove that any rectangle is a cyclic quadrilateral . Given : squarePQRS is rectangle To prove : squarePQRS is cyclic quadrilateral ( ##CTN_MK_MAT_X_P2_GEO_C03_E04_005_Q01.png" width="80%">

Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH . Prove that EFGH is a square.

Prove that the sum of the squares of the diagonals of rhombus is equal to the sum of the squares of the sides.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals