Final answer:
The statements refer to principles and theorems used in geometry to provide a consistent and logical framework for proofs and calculations in the field of mathematics.
Step-by-step explanation:
Understanding the reasons for each statement involves discussing concepts from geometry, which is the branch of mathematics concerned with the properties, measurements, and relationships of points, lines, angles, and surfaces. For example, when we consider that there are three sides to a triangle, and that the sum of their angles is 180 degrees, we are using a fundamental concept in geometry called the Triangle Sum Theorem. This is different from calculations using the Pythagorean Theorem, which allows us to find the length of sides in a right triangle based on the squares of the lengths of the other two sides.
The statements you have mentioned, such as 'alternate interior angles are congruent' or 'side angle side postulate', are all part of the basic principles or postulates in Euclidean geometry. These geometric principles are crucial because they provide a foundation upon which other theorems and properties are built. They ensure consistency and logic in our geometric proofs and calculations, much like the way physical principles must accurately describe the natural world.