## Construct a Square given one side(without using a set square)

**How to construct a square given only one side.**

**What You Start With**

Shown above is the line of any length that is also one side of a square. We want to construct that square.

**Construct A Square given only one length**

- We know without being allowed to use a setsquare to draw vertical lines or a protractor to measure 90°, we are kinda restricted but fortuantely we have covered such scenarios on this website in 'Basic constructions'
- Firstly extend line AB on an extra bit. (Represented in green)
- From point B swing 2 arcs of any distance and where they cross will create points C and B.
- Now we know that point B is the midpoint between points C and D. we also know that when we bisect a line, the bisector cuts the line on the mid point and at 90° as we requre to construct this square.
- So bisect this line and extend the bisector. Take the distance AB on your compass and swing from point B. Where this cuts the bisector creates point F.
- Now we have 2 sides of our square and 3 corners. since we know that a squares sides are all equal, we take our compass and set distance AB and swing from point A and point F.
- Where these two arcs cross gives us our final point (point G) of our square.
- To finished we just join the points to create our square.