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Which of the following is not true for a parallelogram?
- a)Diagonals bisect each other
- b)Opposite sides are equal
- c)Opposite angles are equal
- d)Opposite angles are bisected by the diagonals
Correct answer is option 'D'. Can you explain this answer?
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Which of the following is not true for a parallelogram? a)Diagonals bi...
Understanding Parallelograms
A parallelogram is a special type of quadrilateral with unique properties. Let's explore the properties given in the question.
Properties of a Parallelogram
- Diagonals Bisect Each Other:
This property holds true. In a parallelogram, the diagonals intersect at their midpoints, meaning they bisect each other.
- Opposite Sides are Equal:
This is also true. A fundamental property of parallelograms is that both pairs of opposite sides are of equal length.
- Opposite Angles are Equal:
This statement is true as well. In a parallelogram, opposite angles are always equal in measure.
- Opposite Angles are Bisected by the Diagonals:
This statement is not true. While the diagonals of a parallelogram do bisect each other, they do not bisect the opposite angles. The angles at the intersection of the diagonals are not necessarily equal to half of the opposite angles.
Conclusion
In summary, the only statement that does not hold true in a parallelogram is that the diagonals bisect the opposite angles. Thus, the correct answer is option 'D'. Understanding these properties helps in solving various geometric problems related to parallelograms in Class 9 and beyond.
A parallelogram is a special type of quadrilateral with unique properties. Let's explore the properties given in the question.
Properties of a Parallelogram
- Diagonals Bisect Each Other:
This property holds true. In a parallelogram, the diagonals intersect at their midpoints, meaning they bisect each other.
- Opposite Sides are Equal:
This is also true. A fundamental property of parallelograms is that both pairs of opposite sides are of equal length.
- Opposite Angles are Equal:
This statement is true as well. In a parallelogram, opposite angles are always equal in measure.
- Opposite Angles are Bisected by the Diagonals:
This statement is not true. While the diagonals of a parallelogram do bisect each other, they do not bisect the opposite angles. The angles at the intersection of the diagonals are not necessarily equal to half of the opposite angles.
Conclusion
In summary, the only statement that does not hold true in a parallelogram is that the diagonals bisect the opposite angles. Thus, the correct answer is option 'D'. Understanding these properties helps in solving various geometric problems related to parallelograms in Class 9 and beyond.
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Community Answer
Which of the following is not true for a parallelogram? a)Diagonals bi...
The statement that opposite angles are bisected by the diagonals is not generally true. This property does not hold for every parallelogram; it only occurs in special cases such as a rectangle or a rhombus under certain conditions.
Thus, the option that is not always true for a parallelogram is:
Option D: Opposite angles are bisected by the diagonals.
Option D: Opposite angles are bisected by the diagonals.
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Which of the following is not true for a parallelogram? a)Diagonals bisect each otherb)Opposite sides are equalc)Opposite angles are equald)Opposite angles are bisected by the diagonalsCorrect answer is option 'D'. Can you explain this answer?
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