The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct statement is B.
What is the triangle inequality theorem?
The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
- (a+b) > c
- (b+c) > a
- (c+a) > b
The statements given to us are:
A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
C. The longest side of a triangle is opposite the largest angle.
D. The largest angle of a triangle is between the two longest sides.
As per the triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Hence, the correct statement is B.
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