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Directions: Study the following question carefully and choose the right answer:
Consider the following statements
I. If G is the centroid of ΔABC, then GA = GB = GC.
II. If H is the orthocentre of ΔABC, then HA = HB = HC.
Which of the statements given above is/are correct?
I. If G is the centroid of ΔABC, then GA = GB = GC.
II. If H is the orthocentre of ΔABC, then HA = HB = HC.
Which of the statements given above is/are correct?
- a)Only I
- b)Only II
- c)Both I and II
- d)Neither I nor II
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Directions: Study the following question carefully and choose the righ...
GA = GB = GC is true only and only for equilateral triangle and here it is not given that ABC is an equilateral triangle. So, only for equilateral triangle.
Hence, it is also not correct.
Hence, option D is correct
Hence, it is also not correct.
Hence, option D is correct
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Directions: Study the following question carefully and choose the righ...
Explanation:
Statement I:
- The statement is incorrect.
- In a triangle, the centroid is the point of intersection of the medians.
- The medians meet at a point that divides each median into two segments, with the segment towards the vertex being twice as long as the segment towards the midpoint of the opposite side.
- Therefore, in general, GA ≠ GB ≠ GC.
Statement II:
- The statement is also incorrect.
- The orthocenter of a triangle is the point of intersection of the three altitudes of the triangle.
- The altitudes of a triangle are perpendicular to the sides and intersect them at different points.
- Therefore, in general, HA ≠ HB ≠ HC.
Conclusion:
- Both statements I and II are incorrect.
- Hence, the correct answer is option 'D' - Neither I nor II.
Statement I:
- The statement is incorrect.
- In a triangle, the centroid is the point of intersection of the medians.
- The medians meet at a point that divides each median into two segments, with the segment towards the vertex being twice as long as the segment towards the midpoint of the opposite side.
- Therefore, in general, GA ≠ GB ≠ GC.
Statement II:
- The statement is also incorrect.
- The orthocenter of a triangle is the point of intersection of the three altitudes of the triangle.
- The altitudes of a triangle are perpendicular to the sides and intersect them at different points.
- Therefore, in general, HA ≠ HB ≠ HC.
Conclusion:
- Both statements I and II are incorrect.
- Hence, the correct answer is option 'D' - Neither I nor II.
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Directions: Study the following question carefully and choose the right answer:Consider the following statementsI. If G is the centroid of ΔABC, then GA = GB = GC.II. If H is the orthocentre of ΔABC, then HA = HB = HC.Which of the statements given above is/are correct?a)Only Ib)Only IIc)Both I and IId)Neither I nor IICorrect answer is option 'D'. Can you explain this answer?
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