Class 10 Exam > Class 10 Questions > Direction: In the following questions, A sta...
Start Learning for Free
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AE
Reason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Reason is true : [This is Thale’s Theorem]
For Assertion Since, DE || BC by Thale’s Theorem
Assertion (a) is true
Since, reason gives Assertion.
Free Test
FREE
| Start Free Test |
Community Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion and Reasoning in Geometry
Assertion: If in a ∆ABC, a line DE || BC, intersects AB in D and AC in E, then AB/AD = AC/AE.
Reason: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.
Explanation:
Assertion: AB/AD = AC/AE.
When a line DE is drawn parallel to BC and intersects the sides AB at point D and AC at point E, we can see that the triangles ∆ABC and ∆ADE are similar triangles.
Reason: The other two sides are divided in the same ratio.
Since ∆ABC and ∆ADE are similar triangles, the corresponding sides of these triangles are proportional. In this case, AB and AD are corresponding sides of the triangles, and AC and AE are also corresponding sides.
Therefore, we can express the similarity of these triangles as:
AB/AD = AC/AE
This proves the assertion.
So, both the assertion and the reason are true, and the reason correctly explains the assertion.
Hence, the correct answer is option A: Both A and R are true and R is the correct explanation of A.
Assertion: If in a ∆ABC, a line DE || BC, intersects AB in D and AC in E, then AB/AD = AC/AE.
Reason: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.
Explanation:
Assertion: AB/AD = AC/AE.
When a line DE is drawn parallel to BC and intersects the sides AB at point D and AC at point E, we can see that the triangles ∆ABC and ∆ADE are similar triangles.
Reason: The other two sides are divided in the same ratio.
Since ∆ABC and ∆ADE are similar triangles, the corresponding sides of these triangles are proportional. In this case, AB and AD are corresponding sides of the triangles, and AC and AE are also corresponding sides.
Therefore, we can express the similarity of these triangles as:
AB/AD = AC/AE
This proves the assertion.
So, both the assertion and the reason are true, and the reason correctly explains the assertion.
Hence, the correct answer is option A: Both A and R are true and R is the correct explanation of A.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
Question Description
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AEReason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily