Explanation :
Extending vertex C further away to the left of vertex B in a triangle would create an obtuse triangle. In an obtuse triangle, one of the angles measures greater than 90 degrees. The relationship between the sides and angles in triangles is that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Similarly, the sum of the measures of any two angles of a triangle must be less than 180 degrees.
By extending vertex C further away to the left of vertex B, we can observe the following:
1. The side opposite the obtuse angle (angle C in this case) will be the longest side in the triangle. This is because the longest side is always opposite the largest angle.
2. The sum of the lengths of the two smaller sides will still be greater than the length of the longest side. This verifies the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
3. The sum of the measures of the two smaller angles will be less than 180 degrees. This also verifies the triangle angle-sum theorem, which states that the sum of the measures of the interior angles of a triangle is always 180 degrees.
Overall, extending vertex C further away to the left of vertex B in a triangle confirms the relationship between the sides and angles, specifically with regard to the triangle inequality theorem and the triangle angle-sum theorem.