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If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem?
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If the diagonal of a quadrilateral bisect each other then it is a para...
To prove that a quadrilateral is a parallelogram when its diagonals bisect each other, we can use the following steps:
1. Draw a diagram of the quadrilateral with the diagonals drawn in.
2. Since the diagonals bisect each other, we know that each diagonal is divided into two equal segments. Let's label the points where the diagonals intersect as A and B, and the endpoints of the diagonals as C and D (for the first diagonal) and E and F (for the second diagonal).
3. Since the diagonals divide the quadrilateral into two pairs of congruent triangles, we know that ACD and BEF are congruent triangles.
4. Using the congruence of the triangles, we can prove that opposite sides of the quadrilateral are equal in length. Since AC is congruent to BE and AD is congruent to EF, we know that AC is equal to BE and AD is equal to EF.
5. Since opposite sides of a parallelogram are equal in length, we can conclude that the quadrilateral is a parallelogram.
Therefore, the theorem is proven. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
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If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem?
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If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem? 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 If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem?.
If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem? 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 If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the diagonal of a quadrilateral bisect each other then it is a parallelogram. Proof this theorem?.
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