Class 9 Exam > Class 9 Questions > Direction: In each of the following question...
Start Learning for Free
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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .
Reason : Q is the midpoint of AP.
- 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 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Direction: In each of the following questions, a statement of Asserti...
In ΔABC , E and F are midpoint of the sides AC
View all questions of this test
and AB respectively.
FE || BC [By mid-point theorem]
Now, in ΔABP, F is mid-point of AB and FQ || BP.
Q is mid-point of AP
AQ = QP.
Most Upvoted Answer
Direction: In each of the following questions, a statement of Asserti...
Assertion: In ΔABC, E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q.
Reason: Q is the midpoint of AP.
The given question is about a triangle ABC where E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. We need to determine the relationship between AQ and QP.
To solve this, we can use the concept of midpoints and altitudes in a triangle.
Midpoints in a Triangle:
In a triangle, the line segment joining the midpoints of two sides is parallel to the third side and is half of its length.
Altitude in a Triangle:
The altitude of a triangle is a perpendicular line segment drawn from a vertex to the opposite side (or its extension).
Explanation:
In triangle ABC, E and F are the midpoints of AC and AB respectively. Let's say the altitude AP intersects BC at point D. Now, since E and F are the midpoints, we can say that EF is parallel to BC and EF is half the length of BC.
Since AQ is a line segment on the altitude AP and Q is the midpoint of AP, we can conclude that AQ is half the length of AP. This is because Q is the midpoint of AP and in a triangle, the line segment joining the midpoint of two sides is parallel to the third side and is half of its length.
Similarly, we can say that QP is half the length of PD. This is because Q is the midpoint of AP and PD is the altitude of the triangle, and the line segment joining the midpoint of two sides is parallel to the third side and is half of its length.
Therefore, AQ is half the length of AP, and QP is half the length of PD. Since PD is equal to BC (as PD is the altitude of the triangle), we can conclude that AQ is half the length of AP, and QP is half the length of BC.
Hence, AQ/QP = 1/2.
Reason: Q is the midpoint of AP.
The given question is about a triangle ABC where E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. We need to determine the relationship between AQ and QP.
To solve this, we can use the concept of midpoints and altitudes in a triangle.
Midpoints in a Triangle:
In a triangle, the line segment joining the midpoints of two sides is parallel to the third side and is half of its length.
Altitude in a Triangle:
The altitude of a triangle is a perpendicular line segment drawn from a vertex to the opposite side (or its extension).
Explanation:
In triangle ABC, E and F are the midpoints of AC and AB respectively. Let's say the altitude AP intersects BC at point D. Now, since E and F are the midpoints, we can say that EF is parallel to BC and EF is half the length of BC.
Since AQ is a line segment on the altitude AP and Q is the midpoint of AP, we can conclude that AQ is half the length of AP. This is because Q is the midpoint of AP and in a triangle, the line segment joining the midpoint of two sides is parallel to the third side and is half of its length.
Similarly, we can say that QP is half the length of PD. This is because Q is the midpoint of AP and PD is the altitude of the triangle, and the line segment joining the midpoint of two sides is parallel to the third side and is half of its length.
Therefore, AQ is half the length of AP, and QP is half the length of PD. Since PD is equal to BC (as PD is the altitude of the triangle), we can conclude that AQ is half the length of AP, and QP is half the length of BC.
Hence, AQ/QP = 1/2.
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. Can you explain this answer?
Question Description
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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. 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 , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ QP = .Reason : Q is the midpoint of AP.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 'B'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup