Many home repair and remodeling projects require you to keep square corners square. A square corner has a 90-degree angle. A perfect square or rectangle has four corners that each measure 90 degrees. If the corner angles shift away from 90 degrees, the shape becomes a parallelogram.

Out of Square Picture Frame

Photo by Christina Duart

Pre-hung interior doors are a good example and are a fairly simple project that virtually any homeowner could undertake by themselves. The door is mounted to the hinge jam with hinges, and fastened to the latch jam with a plastic bolt or similar contrivance. The frame is held square by the packaging it is sold in.

Equal diagonal measurements of a square or rectangle will verify that the corners are right angles or 90 degrees. In the picture to the left, the square has four equal sides and each corner is 90 degrees, or a right angle.

Measurements from A to C and from B to D are equal when all the corners are 90 degrees. If one diagonal is longer than the other, the frame is out of square. The corners with the longer diagonal measurement are smaller than 90 degrees, and the other two corners are larger than 90 degrees.

This makes it easy to determine if any rectangular frame is square or needs adjustment.

## The Trick

A Square has Four 90-Degree Corners

If the two diagonal measurements are not equal, just move one of the corners on the longer diagonal toward one of the corners on the shorter diagonal until both measurements are equal.

## Make it Easier

One could measure both diagonals repeatedly until both are equal. This tends to turn into a frustrating dance that takes a lot of time, especially when you're dealing with a door or window frame that you want as perfect as possible. We can simplify by determining what the diagonal measurement should be in the first place. We do this using the Pythagorean Theorem from geometry.

The length of the diagonal side of any right triangle is the square root of the sum of the squares of the two sides. Put simply, side A squared + side B squared = side C squared or A^{2} + B^{2} = C^{2}.

In the rectangle shown, we can easily calculate the expected length of the diagonal with virtually any calculator.

Assume side A is 10 units, and side B is 9 units.

A^{2} = 10 x 10 = 100.

B^{2} = 9 x 9 = 81.

A^{2} + B^{2} = 100 + 81 = 181.

C^{2} = 181.

C = √ 181.

C = 13.45.

## Use The Windows Calculator in Scientific View

Windows Calculator

Enter the length of Side A ---> 10

Press X^{2 } and the display reads 100 (A^{2})

Press +

Enter the length of Side B ---> 9

Press X^{2} and the display reads 81 (B^{2})

Press = and the display reads 181 (A^{2} + B^{2})

Press √ to display the answer 13.45362404707371031716308546217

You don't need all those numbers. Just round it off to two or three digits or 13.45