Question

Show that the diagonals of a rhombus are perpendicular to each other.

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Answer 1

Answer:

Always. The diagonals of a rhombus are always perpendicular. In fact, if the diagonals of a parallelogram are perpendicular bisectors of each other, then it must be a rhombus. In addition to this, a rhombus always has all four congruent sides.

Step-by-step explanation:

Answer 2

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Consider the rhombus as ABCD,

Let the center point be O

Now in triangle AOD and COD,

OA = OC ( Diagonals of IIgm bisect each other )

OD= OD (common )

AD = CD

Therefore, triangle AOD congruent triangle COD

Thus gives ,

Angle AOD = angle COD (cpct)

= 2 AOD = 180°

= AOD = 90°

So , the diagonals of a rhombus are perpendicular to each other.

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