SSC CGL Exam > SSC CGL Questions > In a triangle, if three altitudes are equal, ...
Start Learning for Free
In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)
- a)uilateral
- b)Isoceles
- c)Obtuse
- d)EqRight
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
In a triangle, if three altitudes are equal, then the triangle is (SS...
Let ΔABC is a equilateral triangle of side AB = BC = AC = 2a unit.
AD, BE and CF are three altitudes in the DABC,
In equilateral triangle ∠A = ∠B = ∠C = 60°
Similarly, In ΔACF,
Here, we get AD = BE = CF
Hence, three altitude are equal
Thus, triangle must be a equilateral triangle.
Free Test
FREE
| Start Free Test |
Community Answer
In a triangle, if three altitudes are equal, then the triangle is (SS...
Understanding the Triangle with Equal Altitudes
When three altitudes in a triangle are equal, the triangle must be equilateral. Here's a detailed explanation of why this is true:
Definition of Altitude
- An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.
- In a triangle, the length of the altitude can vary based on the triangle's shape and size.
Implication of Equal Altitudes
- If all three altitudes are equal, it indicates a certain level of symmetry in the triangle.
- This symmetry can only occur in an equilateral triangle, where all sides and angles are equal.
Mathematical Justification
- In an equilateral triangle, since all sides are equal, the altitude from any vertex to the opposite side is the same length.
- For triangles with different side lengths (isosceles or scalene), the altitudes would inherently differ due to the varying base lengths and angles.
Conclusion
- Therefore, the condition of having three equal altitudes leads to the conclusion that the triangle must be equilateral.
- This unique property of equal altitudes is a definitive characteristic of equilateral triangles, ensuring that the correct answer to the question is option 'A': Equilateral.
When three altitudes in a triangle are equal, the triangle must be equilateral. Here's a detailed explanation of why this is true:
Definition of Altitude
- An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.
- In a triangle, the length of the altitude can vary based on the triangle's shape and size.
Implication of Equal Altitudes
- If all three altitudes are equal, it indicates a certain level of symmetry in the triangle.
- This symmetry can only occur in an equilateral triangle, where all sides and angles are equal.
Mathematical Justification
- In an equilateral triangle, since all sides are equal, the altitude from any vertex to the opposite side is the same length.
- For triangles with different side lengths (isosceles or scalene), the altitudes would inherently differ due to the varying base lengths and angles.
Conclusion
- Therefore, the condition of having three equal altitudes leads to the conclusion that the triangle must be equilateral.
- This unique property of equal altitudes is a definitive characteristic of equilateral triangles, ensuring that the correct answer to the question is option 'A': Equilateral.
Attention SSC CGL Students!
To make sure you are not studying endlessly, EduRev has designed SSC CGL study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in SSC CGL.
|
Explore Courses for SSC CGL exam
|
|
Similar SSC CGL Doubts
Top Courses for SSC CGLView all
In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer?
Question Description
In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer?.
In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
Here you can find the meaning of In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)a)uilateralb)Isocelesc)Obtused)EqRightCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice SSC CGL tests.
|
|
Explore Courses for SSC CGL 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