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Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus?
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Show that if a diagonal of a quadrilateral bisected each other and rig...
Let ABCD be a quadrilateral whose diagonals bisect each other at right angles.
Given,
OA = OC, OB = OD and ∠AOB = ∠BOC = ∠OCD = ∠ODA = 90�
To show,
ABCD is parallelogram and AB = BC = CD = AD
Proof,
In ΔAOB and ΔCOB,
OA = OC (Given)
∠AOB = ∠COB (Opposite sides of a parallelogram are equal)
OB = OB (Common)
Therefore, ΔAOB ≅ ΔCOB by SAS congruence condition.
Thus, AB = BC (by CPCT)
Similarly we can prove,
AB = BC = CD = AD
Opposites sides of a quadrilateral are equal hence ABCD is a parallelogram.
Thus, ABCD is rhombus as it is a parallelogram whose diagonals intersect at right angle.
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Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus?
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Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus?.
Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that if a diagonal of a quadrilateral bisected each other and right angles then it is arhombus?.
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