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Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.
Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.
Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.
- a)Assertion and reason are true and reason is the correct explanation of assertion.
- b)Both assertion and reason are true but reason is not the correct explanation of assertion.
- c)Assertion is true but reason is false.
- d)Assertion is false but reason is true.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Direction: In each of the following questions, a statement of Asserti...
Let ABCD be a parallelogram. To show that ABCD is a rectangle, we have to prove that one of its interior angles is 90º.
In ΔABC and ΔDCB,
AB = DC (Opposite sides of a parallelogram are equal)
BC = BC (Common)
AC = DB (Given)
∴ ΔABC ≅ ΔDCB (By SSS Congruence rule)
⇒ ∠ABC = ∠DCB
It is known that the sum of the measures of angles on the same side of transversal is 180º.
∠ABC + ∠DCB = 180º (AB || CD)
⇒ ∠ABC + ∠ABC = 180º
⇒ 2∠ABC = 180º
⇒ ∠ABC = 90º
Since ABCD is a parallelogram and one of its interior angles is 90º, ABCD is a rectangle.
Most Upvoted Answer
Direction: In each of the following questions, a statement of Asserti...
Assertion: If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.
Reason: If the diagonals of a parallelogram are equal, it becomes a rectangle.
The correct answer is option 'A' - Assertion and reason are true, and the reason is the correct explanation of the assertion.
Explanation:
Parallelogram:
A parallelogram is a quadrilateral with opposite sides parallel to each other. In a parallelogram, the opposite angles are equal, and the consecutive angles are supplementary.
Diagonals of a parallelogram:
The diagonals of a parallelogram are the line segments that connect the opposite vertices of the parallelogram. In a parallelogram, the diagonals bisect each other, which means they divide each other into two equal parts.
Assertion:
If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.
Reason:
If the diagonals of a parallelogram are equal, it becomes a rectangle.
Explanation:
To understand why the assertion is true and the reason is the correct explanation, let's consider the properties of a parallelogram and a rectangle.
Properties of a parallelogram:
1. Opposite sides of a parallelogram are parallel.
2. Opposite angles of a parallelogram are equal.
3. Consecutive angles of a parallelogram are supplementary.
4. Diagonals of a parallelogram bisect each other.
Properties of a rectangle:
1. All angles of a rectangle are right angles (90º).
2. Opposite sides of a rectangle are parallel and equal in length.
3. Diagonals of a rectangle are equal in length and bisect each other.
Now, let's analyze the given information:
If the diagonals of a parallelogram ABCD are equal, it means the line segments AC and BD are equal in length.
If the diagonals of a parallelogram are equal, it becomes a rectangle.
From the properties of a rectangle, we know that all angles of a rectangle are right angles (90º).
Therefore, if the diagonals of a parallelogram ABCD are equal, it implies that the angles ∠ABC and ∠ADC are right angles (90º).
Hence, the assertion is true, and the reason is the correct explanation of the assertion.
Conclusion:
If the diagonals of a parallelogram are equal, it becomes a rectangle, and all angles of the parallelogram become right angles (90º). Therefore, the given assertion and reason are true, and the reason correctly explains the assertion.
Reason: If the diagonals of a parallelogram are equal, it becomes a rectangle.
The correct answer is option 'A' - Assertion and reason are true, and the reason is the correct explanation of the assertion.
Explanation:
Parallelogram:
A parallelogram is a quadrilateral with opposite sides parallel to each other. In a parallelogram, the opposite angles are equal, and the consecutive angles are supplementary.
Diagonals of a parallelogram:
The diagonals of a parallelogram are the line segments that connect the opposite vertices of the parallelogram. In a parallelogram, the diagonals bisect each other, which means they divide each other into two equal parts.
Assertion:
If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.
Reason:
If the diagonals of a parallelogram are equal, it becomes a rectangle.
Explanation:
To understand why the assertion is true and the reason is the correct explanation, let's consider the properties of a parallelogram and a rectangle.
Properties of a parallelogram:
1. Opposite sides of a parallelogram are parallel.
2. Opposite angles of a parallelogram are equal.
3. Consecutive angles of a parallelogram are supplementary.
4. Diagonals of a parallelogram bisect each other.
Properties of a rectangle:
1. All angles of a rectangle are right angles (90º).
2. Opposite sides of a rectangle are parallel and equal in length.
3. Diagonals of a rectangle are equal in length and bisect each other.
Now, let's analyze the given information:
If the diagonals of a parallelogram ABCD are equal, it means the line segments AC and BD are equal in length.
If the diagonals of a parallelogram are equal, it becomes a rectangle.
From the properties of a rectangle, we know that all angles of a rectangle are right angles (90º).
Therefore, if the diagonals of a parallelogram ABCD are equal, it implies that the angles ∠ABC and ∠ADC are right angles (90º).
Hence, the assertion is true, and the reason is the correct explanation of the assertion.
Conclusion:
If the diagonals of a parallelogram are equal, it becomes a rectangle, and all angles of the parallelogram become right angles (90º). Therefore, the given assertion and reason are true, and the reason correctly explains the assertion.
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Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?
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Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. 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 Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. 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 Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?.
Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. 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 Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. 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 Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Direction: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct.Assertion : If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90º.Reason : If the diagonals of a parallelogram are equal, it becomes a rectangle.a)Assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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