In rhombus ABCD, diagonal BD is equal to its side a) Prove that triangle ABD is equilateral. b) It is known that BO

| December 21, 2020 | education

In rhombus ABCD, diagonal BD is equal to its side a) Prove that triangle ABD is equilateral. b) It is known that BO = 4cm (O-point of intersection of diagonals). Find the perimeter of the diamond.

a) A rhombus has such a property – all sides of it are equal.
Therefore, since BD is equal to the side of the rhombus, and all its sides are equal, then the diagonal is equal to the other two sides of this triangle.
Hence ABD is equilateral.
b) The diagonals of the rhombus have the property – they are equal and the intersection point is divided in half. Consequently, BO is half of the diagonal BD. So BD = 8 cm. And the condition says that the diagonal is equal to its side, then all sides of the rhombus are equal to 8. Consequently, the perimeter = 4 * 8 = 32cm



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