Final answer:
The Pythagorean theorem is used to calculate the straight-line distance between two points, which can be applied to find distances between vertices in different triangles by identifying the horizontal and vertical distances to form a right triangle.
Step-by-step explanation:
The question is based on the Pythagorean theorem, which is a fundamental principle in geometry. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a² + b² = c². It is used to calculate the distance between two points by forming a right triangle with the horizontal and vertical distances as the two legs, and the straight-line path between the two points as the hypotenuse.
To use the Pythagorean theorem for calculating the distance between vertices in different triangles, you would identify the horizontal and vertical distances between the points (legs a and b) and then use the formula to find the length of the hypotenuse (c), which is the straight-line distance between them.