Determine how the figure helps to verify the triangle inequality theorem.
fill in the blank, captials are the answer choices.
PLEASE HELP

The two sides with lengths of 7 and 5 will _ (MEET A THIRD VERTEX, NEVER MET, ONLY MET WHEN THEY LIE ON THE SIDE) which shows that the _ (DIFFERENCE, SUM) of the lengths of the two sides of a triangle must be ___ (EQUAL TO, GREATER THAN, LESS THAN) the length of the third side.

The two sides with lengths of 7 and 5 will **MEET A THIRD VERTEX** which shows that the **SUM** of the lengths of the two sides of a triangle must be **GREATER THAN** the length of the third side.

Step-by-step explanation:

This statement is a representation of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This is a fundamental property of triangles in Euclidean geometry. So, if you have a triangle with sides of lengths 7 and 5, the length of the third side must be less than 12 (which is the sum of 7 and 5). This theorem helps ensure that a triangle with given side lengths can actually exist. If the sum of the lengths of two sides was equal to or less than the length of the third side, they wouldn't meet to form a triangle. This is why your two sides of lengths 7 and 5 meet at a third vertex to form a triangle.