## Constructing a 90° Angle (without using a set square)

**How to construct an angle of 90° without using a set square or a protractor**

**What you start with**

Shown above is a line of any length. You are aiming to create a new line that will make an angle of 90° to this line.

**Proof:**

- Line AP and BP are congruent because they were both drawn with the same compass width.
- Line AC and BC are congruent because they were both drawn with the same compass width.
- Triangles ∆APC and ∆BPC are congruent becasue they have three sides congruent. Line CP is common to both triangles.
- Angles APC and BPC are congruent because the matching angles of congruent triangles are congruent.
- Angles APC and BPC are both 90 because they lie along a straight line (180) therefore 180 / 2 = 90. Hence meaning Line PC is perpendicular to line that contains AB

A second way of constructing a 90 degree angle is shown by clicking the link below.