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ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must be
- a)Square
- b)Rectangle
- c)Parallelogram
- d)Rhomubs
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must...
Explanation:
In order to prove that ABCD is a parallelogram, we need to show that opposite sides are parallel.
Given:
- AC and BD bisect each other.
Proof:
1. Draw a quadrilateral ABCD.
2. Let AC and BD intersect at point O.
3. Since AC and BD bisect each other, we can say that AO = CO and BO = DO.
4. Now, consider triangle AOB and triangle COD.
- AO = CO (Given)
- BO = DO (Given)
- Angle AOB = Angle COD (Vertical angles)
5. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle AOB and triangle COD are congruent.
6. Therefore, by the Congruent Corresponding Parts of Congruent Triangles (CPCTC) theorem, we can say that AB = CD and BC = AD.
7. Since opposite sides are congruent, we can conclude that ABCD is a parallelogram.
Conclusion:
ABCD is a parallelogram.
Therefore, the correct answer is option C) Parallelogram.
In order to prove that ABCD is a parallelogram, we need to show that opposite sides are parallel.
Given:
- AC and BD bisect each other.
Proof:
1. Draw a quadrilateral ABCD.
2. Let AC and BD intersect at point O.
3. Since AC and BD bisect each other, we can say that AO = CO and BO = DO.
4. Now, consider triangle AOB and triangle COD.
- AO = CO (Given)
- BO = DO (Given)
- Angle AOB = Angle COD (Vertical angles)
5. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle AOB and triangle COD are congruent.
6. Therefore, by the Congruent Corresponding Parts of Congruent Triangles (CPCTC) theorem, we can say that AB = CD and BC = AD.
7. Since opposite sides are congruent, we can conclude that ABCD is a parallelogram.
Conclusion:
ABCD is a parallelogram.
Therefore, the correct answer is option C) Parallelogram.
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Community Answer
ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must...
Simple because the properties match from parllelogram
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ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must bea)Squareb)Rectanglec)Parallelogramd)RhomubsCorrect answer is option 'C'. Can you explain this answer?
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ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must bea)Squareb)Rectanglec)Parallelogramd)RhomubsCorrect answer is option 'C'. Can you explain this answer? 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 ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must bea)Squareb)Rectanglec)Parallelogramd)RhomubsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must bea)Squareb)Rectanglec)Parallelogramd)RhomubsCorrect answer is option 'C'. Can you explain this answer?.
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