Class 9 Exam > Class 9 Questions > Choose the correct statementa)If two sides of...
Start Learning for Free
Choose the correct statement
- a)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.
- b)The sum of the three sides of a triangle is less than the sum of its three medians.
- c)The difference of two sides of a triangle is equal to the third side.
- d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Choose the correct statementa)If two sides of a triangle are unequal t...
Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest, Option D.
Free Test
FREE
| Start Free Test |
Community Answer
Choose the correct statementa)If two sides of a triangle are unequal t...
The Correct Statement: D
The correct statement among the options provided is option D: "Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest." Here's a detailed explanation of why this statement is true.
Understanding the Concept
- When you have a point outside a line, you can draw multiple line segments connecting that point to different points on the line.
- Among all these segments, the perpendicular line segment (the one that meets the line at a right angle) is the shortest.
Proof by Visualization
- Imagine a point P outside a line segment AB. If you draw a line from P to any point C on line AB, you can see that the distance PC varies depending on where point C is located.
- However, if you draw the perpendicular from point P down to line AB, calling this intersection point D, the length PD (the perpendicular) is shorter than any other distance PC for points C on line AB.
Why this is Important
- This property is fundamental in geometry and is often used in various applications, including architecture and engineering, where finding the shortest distance is crucial.
Conclusion
- Hence, option D is accurate, making it the correct choice. The shortest distance from a point to a line is indeed along the perpendicular line drawn from the point to the line.
This understanding lays important groundwork in geometry and distances, essential for higher mathematical concepts.
The correct statement among the options provided is option D: "Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest." Here's a detailed explanation of why this statement is true.
Understanding the Concept
- When you have a point outside a line, you can draw multiple line segments connecting that point to different points on the line.
- Among all these segments, the perpendicular line segment (the one that meets the line at a right angle) is the shortest.
Proof by Visualization
- Imagine a point P outside a line segment AB. If you draw a line from P to any point C on line AB, you can see that the distance PC varies depending on where point C is located.
- However, if you draw the perpendicular from point P down to line AB, calling this intersection point D, the length PD (the perpendicular) is shorter than any other distance PC for points C on line AB.
Why this is Important
- This property is fundamental in geometry and is often used in various applications, including architecture and engineering, where finding the shortest distance is crucial.
Conclusion
- Hence, option D is accurate, making it the correct choice. The shortest distance from a point to a line is indeed along the perpendicular line drawn from the point to the line.
This understanding lays important groundwork in geometry and distances, essential for higher mathematical concepts.
|
Explore Courses for Class 9 exam
|
|
Top Courses for Class 9View all
Question Description
Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer?.
Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. 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 Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Choose the correct statementa)If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.b)The sum of the three sides of a triangle is less than the sum of its three medians.c)The difference of two sides of a triangle is equal to the third side.d)Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 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