if the diagonals of a parallelogram are equal then show that it is a rectangle
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Hey there!
★ Given: Diagonals AC and BD of parallelogram
AC=BD.
★ Consider triangles ABD and ACD.
AC = BD [Given]
AB = DC [Opposite sides of a parallelogram]
AD = AD [Common side]
∴ ΔABD ≅ ΔDCA [SSS congruence criterion]
∠BAD = ∠CDA [CPCT]
∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]
So, ∠BAD and ∠CDA are right angles as they are congruent and supplementary.
Therefore,
Parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.
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★ Given: Diagonals AC and BD of parallelogram
AC=BD.
★ Consider triangles ABD and ACD.
AC = BD [Given]
AB = DC [Opposite sides of a parallelogram]
AD = AD [Common side]
∴ ΔABD ≅ ΔDCA [SSS congruence criterion]
∠BAD = ∠CDA [CPCT]
∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]
So, ∠BAD and ∠CDA are right angles as they are congruent and supplementary.
Therefore,
Parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.
HOPE IT HELPED ^_^
#EshanSingh1
#brainly star
#follow me
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Hi dear here is your answer.
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