## Parallel Line Through a Point

**How to draw a Parallel line through a point**

**What You Start With**

Shown above is a line of any length and a Point P. Point P can also be placed below the line for the same principles to work.

**The Theory Behind How it Works**

**Proof:**

- Line segment AB and PD are congruent because they were both drawn with the same compass width.
- Line segment AC and PE are congruent because they were both drawn with the same compass width.
- Line segment BC and DE are congruent because they were both drawn with the same compass width.
- Therefore triangles ∆ABC and ∆PDE are congruent because they have 3 sides congruent.
- Angle BAC and DPE are congruent because corresponding angles of congruent triangles are congruent.
- The line AD is is drawn with a straight edge and cuts across lines AC and PE.
- Lines AC and PE are corresponding angles that are equal in measure, therefore line FG and HI are parallel.