prove that diognals of rectangle are bisects each other
Answers
Thus diagonals bisect each other in a rectangle . ∴ The diagonals of a rectangle bisects each other and equal .
Answer:
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Class 11
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>>Prove that the diagonals of a rectangle
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Prove that the diagonals of a rectangle bisect each other and are equal.
Medium
Solution
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Let OABC is a rectangle and O(0,0),A(a,0),B(a,b) and C(0,6)
Let diagonal OB and AC bisects each other at point P.
Co-ordinate of midpoint P of diagonal
OB=(
2
(0+a)
,
2
(0+b)
)
=(
2
a
,
2
b
)
Co-ordinate of mid point of P diagonal
AC=(
2
(a+0)
,
2
(0+b)
)
=(
2
a
,
2
b
)
Clearly diagonal rectangle bisects each other at point P.
again, OB=
(a−0)
2
+(b−0)
2
=
a
2
+b
2
and AC=
(0−a)
2
+(b−0)
2
Clearly OB=AC
Hence length of diagonals of rectangle are equal
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