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Which among the following is used to construct a triangle?
- a)The lengths of the three sides.
- b)The perimeter of the triangle.
- c)The measures of three angles.
- d)The names of three vertices.
Correct answer is option 'A'. Can you explain this answer?
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Which among the following is used to construct a triangle?a)The length...
S.S.S. criterion can be used indirectly to construct a triangle given the lengths of its three sides.
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Which among the following is used to construct a triangle?a)The length...
Introduction:
To construct a triangle, we need certain information or measurements. Among the given options, the correct answer is option 'A', which states that the lengths of the three sides are used to construct a triangle. In this response, we will explain why this is the correct answer.
Explanation:
To construct a triangle, we need to have specific measurements that satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's discuss why the other options are not correct:
b) The perimeter of the triangle:
The perimeter of a triangle is the sum of the lengths of all three sides. While knowing the perimeter is useful, it does not provide enough information to construct a triangle since there are multiple combinations of side lengths that can have the same perimeter.
c) The measures of three angles:
Knowing the measures of the three angles is not enough to construct a triangle. This is because different combinations of angles can result in different shapes, such as obtuse, acute, or right-angled triangles. The angles alone do not determine the lengths of the sides.
d) The names of three vertices:
The names of three vertices only provide the locations or labels of points in space. They do not provide any information about the lengths of the sides or the shape of the triangle.
Conclusion:
To construct a triangle, we need to know the lengths of the three sides. This information allows us to apply the triangle inequality theorem and ensure that the sum of any two sides is greater than the length of the third side. This condition is necessary to form a valid triangle.
To construct a triangle, we need certain information or measurements. Among the given options, the correct answer is option 'A', which states that the lengths of the three sides are used to construct a triangle. In this response, we will explain why this is the correct answer.
Explanation:
To construct a triangle, we need to have specific measurements that satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's discuss why the other options are not correct:
b) The perimeter of the triangle:
The perimeter of a triangle is the sum of the lengths of all three sides. While knowing the perimeter is useful, it does not provide enough information to construct a triangle since there are multiple combinations of side lengths that can have the same perimeter.
c) The measures of three angles:
Knowing the measures of the three angles is not enough to construct a triangle. This is because different combinations of angles can result in different shapes, such as obtuse, acute, or right-angled triangles. The angles alone do not determine the lengths of the sides.
d) The names of three vertices:
The names of three vertices only provide the locations or labels of points in space. They do not provide any information about the lengths of the sides or the shape of the triangle.
Conclusion:
To construct a triangle, we need to know the lengths of the three sides. This information allows us to apply the triangle inequality theorem and ensure that the sum of any two sides is greater than the length of the third side. This condition is necessary to form a valid triangle.
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Which among the following is used to construct a triangle?a)The length...
Answer:-(A) The lengths of the three sides
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Which among the following is used to construct a triangle?a)The lengths of the three sides. b)The perimeter of the triangle.c)The measures of three angles.d)The names of three vertices.Correct answer is option 'A'. Can you explain this answer?
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