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In which of the following cases is the construction of a triangle not possible?
- a)Measures of 3 sides are given.
- b)Measures of 2 sides and an included angle are given.
- c)Measures of 2 angles and a side are given.
- d)Measures of 3 angles are given.
Correct answer is option 'D'. Can you explain this answer?
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In which of the following cases is the construction of a triangle not ...
Unless and until you know length of one side you cannot tell at what distance the angles have to be drawn.
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In which of the following cases is the construction of a triangle not ...
Knowing only angle-angle-angle (AAA) does not work
because it can produce
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In which of the following cases is the construction of a triangle not ...
Explanation:
In order to construct a triangle, we need to 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.
a) Measures of 3 sides are given:
If the measures of all three sides are given, we can determine if a triangle can be constructed by applying the triangle inequality theorem. If the sum of the lengths of any two sides is greater than the length of the third side, then a triangle can be constructed. Therefore, this case allows for the construction of a triangle.
b) Measures of 2 sides and an included angle are given:
If the measures of two sides and the included angle between them are given, we can use the Law of Cosines to determine if a triangle can be constructed. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of their lengths and the cosine of the included angle. If the calculated value for one side is positive, then a triangle can be constructed. Therefore, this case allows for the construction of a triangle.
c) Measures of 2 angles and a side are given:
If the measures of two angles and a side are given, we can use the Law of Sines to determine if a triangle can be constructed. The Law of Sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant. If the calculated values for the other two sides are positive, then a triangle can be constructed. Therefore, this case allows for the construction of a triangle.
d) Measures of 3 angles are given:
If the measures of all three angles are given, we cannot determine the lengths of the sides of the triangle. The measures of the angles alone do not provide enough information to determine the lengths of the sides, and therefore, we cannot construct a triangle with only the measures of the angles. Therefore, this case does not allow for the construction of a triangle.
Conclusion:
The construction of a triangle is not possible when the measures of all three angles are given (option D).
In order to construct a triangle, we need to 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.
a) Measures of 3 sides are given:
If the measures of all three sides are given, we can determine if a triangle can be constructed by applying the triangle inequality theorem. If the sum of the lengths of any two sides is greater than the length of the third side, then a triangle can be constructed. Therefore, this case allows for the construction of a triangle.
b) Measures of 2 sides and an included angle are given:
If the measures of two sides and the included angle between them are given, we can use the Law of Cosines to determine if a triangle can be constructed. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of their lengths and the cosine of the included angle. If the calculated value for one side is positive, then a triangle can be constructed. Therefore, this case allows for the construction of a triangle.
c) Measures of 2 angles and a side are given:
If the measures of two angles and a side are given, we can use the Law of Sines to determine if a triangle can be constructed. The Law of Sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant. If the calculated values for the other two sides are positive, then a triangle can be constructed. Therefore, this case allows for the construction of a triangle.
d) Measures of 3 angles are given:
If the measures of all three angles are given, we cannot determine the lengths of the sides of the triangle. The measures of the angles alone do not provide enough information to determine the lengths of the sides, and therefore, we cannot construct a triangle with only the measures of the angles. Therefore, this case does not allow for the construction of a triangle.
Conclusion:
The construction of a triangle is not possible when the measures of all three angles are given (option D).
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In which of the following cases is the construction of a triangle not possible?a)Measures of 3 sides are given.b)Measures of 2 sides and an included angle are given.c)Measures of 2 angles and a side are given.d)Measures of 3 angles are given.Correct answer is option 'D'. Can you explain this answer?
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