When we are provided with two sides of a triangle and the included angle (the angle between the two sides), we can determine a unique triangle using this information based on geometric principles. This is known as the Side-Angle-Side (SAS) Postulate in geometry, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Since a triangle can only have one unique set of sides and angles, knowing the lengths of two sides and the measure of the included angle means there is only one way to construct such a triangle. The SAS Postulate essentially guarantees that there is no ambiguity in constructing this triangle.
Therefore, the correct answer to how many different triangles can be constructed using these measurements is:
○ B. 1
Only one unique triangle can be made with the given side lengths of 10 centimeters and 8 centimeters and the angle between them.
