Question

question 1 of 5
select the correct answer.
how does the figure verify the triangle inequality theorem?
by showing that the sides with lengths of 7 and 4 will never meet
by showing that the sides with lengths of 7 and 4 can meet to form a third vertex
by showing that the sides with lengths of 7 and 4 can form many possible triangles
by showing that the sides with lengths of 7 and 4 will only meet when they lie on the third side

Explanation:

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Here, \(7 + 4=11\), which means the two sides (lengths \(7\) and \(4\)) do not satisfy the triangle inequality (\(a + b>c\) where \(a = 7\), \(b = 4\), \(c = 11\)). In geometric construction (using arcs to represent side lengths), when \(a + b=c\), the arcs (representing sides \(a\) and \(b\)) will be tangent to each other at a point on the third - side (length \(c\)) line, indicating that the two non - base sides will only meet when they lie on the third side.

Answer:

by showing that the sides with lengths of 7 and 4 will only meet when they lie on the third side