Class 9 Exam > Class 9 Questions > Which of the following is incorrect ?a)If two...
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Which of the following is incorrect ?
- a)If two angles of a triangle are unequal, then the greater angle has the greater side opposite to it
- b)Sum of any two sides of a triangle is greater than twice the median drawn to the third side
- c)The sum of any two sides of a triangle is always greater than the third side
- d)Sum of the three sides of a triangle is less than the sum of its three medians
Correct answer is option 'D'. Can you explain this answer?
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Which of the following is incorrect ?a)If two angles of a triangle are...
Explanation:
To determine which statement is incorrect, let's analyze each option:
a) If two angles of a triangle are unequal, then the greater angle has the greater side opposite to it:
This statement is correct. According to the triangle inequality theorem, the side opposite the greater angle is always longer than the side opposite the smaller angle.
b) Sum of any two sides of a triangle is greater than twice the median drawn to the third side:
This statement is correct. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Additionally, the median drawn to the third side divides it into two segments, and the sum of the lengths of these two segments is always greater than the length of the median.
c) The sum of any two sides of a triangle is always greater than the third side:
This statement is correct. As mentioned earlier, according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
d) Sum of the three sides of a triangle is less than the sum of its three medians:
This statement is incorrect. The sum of the lengths of the three sides of a triangle is always greater than the sum of the lengths of its three medians. The sum of the medians is equal to three-fourths of the perimeter of the triangle.
Therefore, the correct answer is option 'D' as it contradicts the triangle inequality theorem.
To determine which statement is incorrect, let's analyze each option:
a) If two angles of a triangle are unequal, then the greater angle has the greater side opposite to it:
This statement is correct. According to the triangle inequality theorem, the side opposite the greater angle is always longer than the side opposite the smaller angle.
b) Sum of any two sides of a triangle is greater than twice the median drawn to the third side:
This statement is correct. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Additionally, the median drawn to the third side divides it into two segments, and the sum of the lengths of these two segments is always greater than the length of the median.
c) The sum of any two sides of a triangle is always greater than the third side:
This statement is correct. As mentioned earlier, according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
d) Sum of the three sides of a triangle is less than the sum of its three medians:
This statement is incorrect. The sum of the lengths of the three sides of a triangle is always greater than the sum of the lengths of its three medians. The sum of the medians is equal to three-fourths of the perimeter of the triangle.
Therefore, the correct answer is option 'D' as it contradicts the triangle inequality theorem.
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Which of the following is incorrect ?a)If two angles of a triangle are unequal, then the greater angle has the greater side opposite to itb)Sum of any two sides of a triangle is greater than twice the median drawn to the third sidec)The sum of any two sides of a triangle is always greater than the third sided)Sum of the three sides of a triangle is less than the sum of its three mediansCorrect answer is option 'D'. Can you explain this answer?
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