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In which of the following cases can a triangle be constructed?
- a)Measures of three sides are given.
- b)Measures of two sides and an included angle are given.
- c)Measures of two angles and the side between them are given.
- d)All the above.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In which of the following cases can a triangle be constructed?a)Measur...
Introduction:
A triangle is a closed figure with three sides and three angles. In order to construct a triangle, certain conditions must be met. Let's analyze the given options to determine which conditions are sufficient for constructing a triangle.
a) Measures of three sides are given:
If the measures of all three sides of a triangle are given, a triangle can be constructed. This is because the three sides will connect to form a closed figure, satisfying the definition of a triangle. Additionally, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side according to the triangle inequality theorem.
b) Measures of two sides and an included angle are given:
If the measures of two sides and the included angle between them are given, a triangle can also be constructed. This is known as the Side-Angle-Side (SAS) condition. The two given sides can be extended from their common vertex to form the other two sides of the triangle, and the given angle can be placed between these sides. This forms a closed figure, satisfying the definition of a triangle.
c) Measures of two angles and the side between them are given:
If the measures of two angles and the side between them are given, a triangle can be constructed. This is known as the Angle-Side-Angle (ASA) condition. One of the given angles can be placed at a vertex, and the side adjacent to this angle can be drawn. Then, the other given angle can be placed adjacent to the first angle, and the remaining side can be drawn to connect the two angles. This forms a closed figure, satisfying the definition of a triangle.
Conclusion:
From the above analysis, it is evident that a triangle can be constructed in all of the given cases: when the measures of three sides are given, when the measures of two sides and an included angle are given, and when the measures of two angles and the side between them are given. Therefore, the correct answer is option 'D' - all of the above cases allow for the construction of a triangle.
A triangle is a closed figure with three sides and three angles. In order to construct a triangle, certain conditions must be met. Let's analyze the given options to determine which conditions are sufficient for constructing a triangle.
a) Measures of three sides are given:
If the measures of all three sides of a triangle are given, a triangle can be constructed. This is because the three sides will connect to form a closed figure, satisfying the definition of a triangle. Additionally, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side according to the triangle inequality theorem.
b) Measures of two sides and an included angle are given:
If the measures of two sides and the included angle between them are given, a triangle can also be constructed. This is known as the Side-Angle-Side (SAS) condition. The two given sides can be extended from their common vertex to form the other two sides of the triangle, and the given angle can be placed between these sides. This forms a closed figure, satisfying the definition of a triangle.
c) Measures of two angles and the side between them are given:
If the measures of two angles and the side between them are given, a triangle can be constructed. This is known as the Angle-Side-Angle (ASA) condition. One of the given angles can be placed at a vertex, and the side adjacent to this angle can be drawn. Then, the other given angle can be placed adjacent to the first angle, and the remaining side can be drawn to connect the two angles. This forms a closed figure, satisfying the definition of a triangle.
Conclusion:
From the above analysis, it is evident that a triangle can be constructed in all of the given cases: when the measures of three sides are given, when the measures of two sides and an included angle are given, and when the measures of two angles and the side between them are given. Therefore, the correct answer is option 'D' - all of the above cases allow for the construction of a triangle.
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Community Answer
In which of the following cases can a triangle be constructed?a)Measur...
As you know :-
A) Measures of three sides are given means SSS Property of Triangle.
B) Measures of two sides and an angle included means SAS Property of Triangle.
C) Measures of two angles and the side between them are given means ASA Property of Triangle
That's why in all the three cases construction of triangle is possible.
A) Measures of three sides are given means SSS Property of Triangle.
B) Measures of two sides and an angle included means SAS Property of Triangle.
C) Measures of two angles and the side between them are given means ASA Property of Triangle
That's why in all the three cases construction of triangle is possible.
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In which of the following cases can a triangle be constructed?a)Measures of three sides are given.b)Measures of two sides and an included angle are given.c)Measures of two angles and the side between them are given.d)All the above. Correct answer is option 'D'. Can you explain this answer?
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