Question

if you are given a quad. and you are said to prove it as a rhombus....then what are the criterions you have to prove.........​

Answer 1

If you have to prove that a quadrilateral is a rhombus then you need to show that all the sides of the quadrilateral are equal.

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@zaqwertyuioplm :)

Answer 2

Answer:

If all sides of a quadrilateral are congruent, then it’s a rhombus (reverse of the definition).

If the diagonals of a quadrilateral bisect all the angles, then it’s a rhombus (converse of a property).

If the diagonals of a quadrilateral are perpendicular bisectors of each other, then it’s a rhombus (converse of a property).

Tip: To visualize this one, take two pens or pencils of different lengths and make them cross each other at right angles and at their midpoints. Their four ends must form a diamond shape — a rhombus.

If two consecutive sides of a parallelogram are congruent, then it’s a rhombus (neither the reverse of the definition nor the converse of a property).

If either diagonal of a parallelogram bisects two angles, then it’s a rhombus (neither the reverse of the definition nor the converse of a property).

If the diagonals of a parallelogram are perpendicular, then it’s a rhombus (neither the reverse of the definition nor the converse of a property).