How to Construct the Mid Point of a Line Segment

In this video presentation, Chris Tisdell introduces a geometric construction method using a circle arc template and a straightedge to find the midpoint of a given line segment. He begins by explaining the limitations of compasses and introduces his circle arc template as a replacement. The goal is to find the midpoint, a problem with a long history.

The circle arc template consists of a positionable centre point and the ability to draw an arc of about 300 degrees, accompanied by a straight edge. Chris demonstrates the construction step by step. First, he constructs an equilateral triangle below the line segment AB by placing the centre at one endpoint and making an arc. This process creates anew point, which he labels as C. Then, he repeats the procedure by placing the center at C and drawing another arc, resulting in a new point D.

Chris emphasises that these markings on the tools are not essential for the construction but can be helpful. He then demonstrates a similar process but constructs an equilateral triangle above the line segment AB, yielding points E and F.

To find the midpoint of AB, Chris connects points D and F, resulting in a new point G. He claims that AG is equal in length to BG, which proves that G is the midpoint of AB.

For justification, he employs the concept of congruent triangles. He shows that triangles ADC and BFE are congruent due to the side-side-side rule. This congruence allows him to deduce that angles and corresponding sides within these triangles are equal. Subsequently, he establishes congruence between triangles GAD and GBF, ultimately proving thatAG and BG are equal in length and that G is the midpoint of AB.

Chris concludes the presentation by highlighting the perpendicular bisector property of this construction and its versatility in various geometrical scenarios.