Class 9 Exam > Class 9 Questions > Choose the correct statementa)A trapezoid is ...
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Choose the correct statement
- a)A trapezoid is a parallelogram.
- b)The diagonals of a parallelogram are congruent, if it is a rectangle.
- c)If one pair of opposite sides of a quadrilateral are parallel the quadrilateral is called a parallelogram
- d)Diagonals of a square are not equal.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Choose the correct statementa)A trapezoid is a parallelogram.b)The dia...
**Explanation:**
A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. It has several properties, one of which is that its diagonals bisect each other. In other words, the diagonals of a parallelogram divide each other into two equal parts.
On the other hand, a rectangle is a type of parallelogram that has four right angles. Since a rectangle is a special case of a parallelogram, it shares all of the properties of a parallelogram, including the fact that its diagonals bisect each other. Therefore, the statement that the diagonals of a parallelogram are congruent if it is a rectangle is correct.
Let's analyze the other options:
a) A trapezoid is a quadrilateral with one pair of opposite sides that are parallel. Unlike a parallelogram, a trapezoid does not have the property of having opposite sides that are congruent. Therefore, a trapezoid is not a parallelogram, and the statement is incorrect.
c) If one pair of opposite sides of a quadrilateral are parallel, the quadrilateral is called a trapezoid, not a parallelogram. A parallelogram must have both pairs of opposite sides parallel. Therefore, the statement is incorrect.
d) A square is a special type of rectangle in which all four sides are equal in length and all four angles are right angles. Since a square is a special case of a rectangle, it shares all of the properties of a rectangle, including the fact that its diagonals bisect each other. Therefore, the statement that the diagonals of a square are not equal is incorrect.
In conclusion, the correct statement is option B, which states that the diagonals of a parallelogram are congruent if it is a rectangle.
A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. It has several properties, one of which is that its diagonals bisect each other. In other words, the diagonals of a parallelogram divide each other into two equal parts.
On the other hand, a rectangle is a type of parallelogram that has four right angles. Since a rectangle is a special case of a parallelogram, it shares all of the properties of a parallelogram, including the fact that its diagonals bisect each other. Therefore, the statement that the diagonals of a parallelogram are congruent if it is a rectangle is correct.
Let's analyze the other options:
a) A trapezoid is a quadrilateral with one pair of opposite sides that are parallel. Unlike a parallelogram, a trapezoid does not have the property of having opposite sides that are congruent. Therefore, a trapezoid is not a parallelogram, and the statement is incorrect.
c) If one pair of opposite sides of a quadrilateral are parallel, the quadrilateral is called a trapezoid, not a parallelogram. A parallelogram must have both pairs of opposite sides parallel. Therefore, the statement is incorrect.
d) A square is a special type of rectangle in which all four sides are equal in length and all four angles are right angles. Since a square is a special case of a rectangle, it shares all of the properties of a rectangle, including the fact that its diagonals bisect each other. Therefore, the statement that the diagonals of a square are not equal is incorrect.
In conclusion, the correct statement is option B, which states that the diagonals of a parallelogram are congruent if it is a rectangle.
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Community Answer
Choose the correct statementa)A trapezoid is a parallelogram.b)The dia...
When the diagonals of rectangle bisect, they are equal to one another which means that they form congruent triangles.
So, option 'b' is correct.
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Choose the correct statementa)A trapezoid is a parallelogram.b)The diagonals of a parallelogram are congruent, if it is a rectangle.c)If one pair of opposite sides of a quadrilateral are parallel the quadrilateral is called a parallelogramd)Diagonals of a square are not equal.Correct answer is option 'B'. Can you explain this answer?
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