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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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.
Reason : Diagonals AX and BC bisect each other at right angles.
- 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 'C'. Can you explain this answer?
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Verified Answer
Direction: In each of the following questions, a statement of Asserti...
In quadrilateral ABXC , we have
View all questions of this test
AD = DX [Given]
BD = DC [Given]
So, diagonals AX and BC bisect each other but not
at right angles.
Therefore, ABXC is a parallelogram
Most Upvoted Answer
Direction: In each of the following questions, a statement of Asserti...
Assertion: In ΔABC, median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.
Reason: Diagonals AX and BC bisect each other at right angles.
Explanation:
To prove that ABXC is a parallelogram, we need to show that opposite sides are parallel and equal in length.
Proof:
1. Given that AD is the median of triangle ABC, which means it divides the side BC into two equal parts.
2. Let's consider point X on the line AD produced such that AD = DX.
3. Since AD = DX, it implies that AX is also equal to XD.
4. Now, we need to prove that AB || XC and BC || AX.
5. To prove AB || XC, we can use the property that the medians of a triangle divide each other in the ratio 2:1.
6. Since AD is a median, it divides side BC into two equal parts. So, BD = DC.
7. Now, consider triangles ABD and XDC. We have AD = DX (given) and BD = DC (proved in the previous step).
8. By the side-side-side congruence criterion, we can say that triangle ABD is congruent to triangle XDC.
9. Therefore, angle ABD = angle XDC and angle DAB = angle DCX.
10. These angles are alternate interior angles, and when a transversal intersects two parallel lines, alternate interior angles are congruent.
11. Thus, AB || XC.
12. Similarly, we can prove that BC || AX using the same logic.
13. Now, we have AB || XC and BC || AX, which means ABXC is a parallelogram.
14. Therefore, the assertion is true.
Conclusion:
The assertion is true because we have proved that ABXC is a parallelogram by showing that its opposite sides are parallel. However, the reason provided is false because the diagonals AX and BC do not necessarily bisect each other at right angles.
Reason: Diagonals AX and BC bisect each other at right angles.
Explanation:
To prove that ABXC is a parallelogram, we need to show that opposite sides are parallel and equal in length.
Proof:
1. Given that AD is the median of triangle ABC, which means it divides the side BC into two equal parts.
2. Let's consider point X on the line AD produced such that AD = DX.
3. Since AD = DX, it implies that AX is also equal to XD.
4. Now, we need to prove that AB || XC and BC || AX.
5. To prove AB || XC, we can use the property that the medians of a triangle divide each other in the ratio 2:1.
6. Since AD is a median, it divides side BC into two equal parts. So, BD = DC.
7. Now, consider triangles ABD and XDC. We have AD = DX (given) and BD = DC (proved in the previous step).
8. By the side-side-side congruence criterion, we can say that triangle ABD is congruent to triangle XDC.
9. Therefore, angle ABD = angle XDC and angle DAB = angle DCX.
10. These angles are alternate interior angles, and when a transversal intersects two parallel lines, alternate interior angles are congruent.
11. Thus, AB || XC.
12. Similarly, we can prove that BC || AX using the same logic.
13. Now, we have AB || XC and BC || AX, which means ABXC is a parallelogram.
14. Therefore, the assertion is true.
Conclusion:
The assertion is true because we have proved that ABXC is a parallelogram by showing that its opposite sides are parallel. However, the reason provided is false because the diagonals AX and BC do not necessarily bisect each other at right angles.
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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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 '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 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 '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 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 '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 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 '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 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. Can you explain this answer?, a detailed solution 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. Can you explain this answer? has been provided alongside types of 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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 : In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.Reason : Diagonals AX and BC bisect each other at right angles.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 'C'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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