If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Solution:
Let’s suppose that we have a parallelogram ABCD with AC=BC.
We need to prove that it is a rectangle.
In
and
(Given)
(Opposite sides of a parallelogram are equal)
(Common)
Therefore, by SSS congruence rule,
It means we have,
(Corresponding parts of congruent triangles are equal) (1)
But ,we also have
(Co-interior angles because
)
Putting (1) in the above equation, we get
Similarly, we can prove that all the angles of a given parallelogram ABCD are
but there is no need to do so because once we have proved that one angle is equal to
in a given parallelogram then it can be considered as rectangle.
Therefore, ABCD is a rectangle.
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