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A parallelogram must be a rectangle if its diagonals
- a)bisect the angles to which they are drawn
- b)are perpendicular to each other
- c)bisect each other
- d)are congruent
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A parallelogram must be a rectangle if its diagonalsa)bisect the angle...
Explanation:
A parallelogram is a quadrilateral with opposite sides parallel to each other. It has several properties that distinguish it from other types of quadrilaterals. One of these properties is that its diagonals bisect each other.
In a parallelogram, the diagonals divide each other into two equal parts. This means that the two line segments that make up each diagonal are congruent. Therefore, the correct answer is option D, which states that the diagonals are congruent.
Why the Other Options are Incorrect:
Option A: If the diagonals bisect the angles to which they are drawn, it means that each diagonal divides one of the angles of the parallelogram into two equal parts. However, this property is not sufficient to prove that the parallelogram is a rectangle.
Option B: If the diagonals are perpendicular to each other, it means that the parallelogram is a rectangle, but this is not always the case. For example, a rhombus is a parallelogram with four equal sides, but its diagonals are perpendicular to each other without being a rectangle.
Option C: If the diagonals bisect each other, it means that they intersect at their midpoint. However, this property is not sufficient to prove that the parallelogram is a rectangle.
Conclusion:
In conclusion, a parallelogram must have diagonals that are congruent to be a rectangle. This property is one of the defining characteristics of a rectangle and is essential to its definition.
A parallelogram is a quadrilateral with opposite sides parallel to each other. It has several properties that distinguish it from other types of quadrilaterals. One of these properties is that its diagonals bisect each other.
In a parallelogram, the diagonals divide each other into two equal parts. This means that the two line segments that make up each diagonal are congruent. Therefore, the correct answer is option D, which states that the diagonals are congruent.
Why the Other Options are Incorrect:
Option A: If the diagonals bisect the angles to which they are drawn, it means that each diagonal divides one of the angles of the parallelogram into two equal parts. However, this property is not sufficient to prove that the parallelogram is a rectangle.
Option B: If the diagonals are perpendicular to each other, it means that the parallelogram is a rectangle, but this is not always the case. For example, a rhombus is a parallelogram with four equal sides, but its diagonals are perpendicular to each other without being a rectangle.
Option C: If the diagonals bisect each other, it means that they intersect at their midpoint. However, this property is not sufficient to prove that the parallelogram is a rectangle.
Conclusion:
In conclusion, a parallelogram must have diagonals that are congruent to be a rectangle. This property is one of the defining characteristics of a rectangle and is essential to its definition.
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Community Answer
A parallelogram must be a rectangle if its diagonalsa)bisect the angle...
From theorem 16.5, if diagonals of parallelogram are congruent then it is a rectangle
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A parallelogram must be a rectangle if its diagonalsa)bisect the angles to which they are drawnb)are perpendicular to each otherc)bisect each otherd)are congruentCorrect answer is option 'D'. Can you explain this answer?
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