Question

question 1 of 10
which of the following is the statement of the triangle inequality theorem?
a. the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
b. the sum of the measures of any two angles of a triangle is greater than the measure of the third angle.
c. the largest angle of a triangle is between the two longest sides.
d. the longest side of a triangle is opposite the largest angle.

Explanation:

The triangle inequality theorem specifically pertains to the relationship between the lengths of the sides of a triangle. Option A correctly states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Option B is incorrect as it refers to angles instead of sides. Option C is not the triangle inequality theorem. Option D is about the relationship between side lengths and angle measures (a different geometric property, not the triangle inequality theorem).

Answer:

A. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.