What length should be checked in squares and rectangles to ensure corners form a right angle after establishing building lines?

To confirm that corners form a right angle in squares and rectangles after the building lines have been established, it is essential to check the diagonals. This is based on the geometric principle known as the Pythagorean theorem, which states that in a rectangle (or square), the relationship between the lengths of the sides and the diagonals can be described as follows: the square of the length of one diagonal is equal to the sum of the squares of the lengths of the other two sides.

For instance, when measuring the diagonals of a rectangle, if both diagonals are equal in length, it confirms that the corners are at right angles. This method is vital in carpentry and construction for ensuring structures are square and stable, which directly affects the integrity and aesthetic of the finished work.

While checking lines, perimeters, and footings serves important functions in construction, they do not specifically verify the right angles of corners. Checking lines ensures straightness, perimeters provide total length measurement, and footings relate to foundation stability, but it is through the verification of diagonal measurements that one can affirm the accuracy of corner angles in squares and rectangles.