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Question
Which of the following criteria cannot be used to construct a unique triangle?
Which of the following criteria cannot be used to construct a unique triangle?
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Solution
The correct option is C AAA
If we know two angles of a triangle and the side between these angles, we can construct the triangle using the ASA criterion.
Similarly, if we know two sides and the included angle, then we can construct a triangle using the SAS criterion.
If we know all the three sides of the triangle, we can construct the triangle using the SSS criterion.
In all of these methods, we can always construct a unique triangle.
But if we only know the measure of the three angles of a triangle, we cannot construct a unique triangle as we can construct an infinite number of triangles with different side lengths.
If we know two angles of a triangle and the side between these angles, we can construct the triangle using the ASA criterion.
Similarly, if we know two sides and the included angle, then we can construct a triangle using the SAS criterion.
If we know all the three sides of the triangle, we can construct the triangle using the SSS criterion.
In all of these methods, we can always construct a unique triangle.
But if we only know the measure of the three angles of a triangle, we cannot construct a unique triangle as we can construct an infinite number of triangles with different side lengths.
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