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