Thales theorem

A very funny way of explaining Thales Theorem:

Dividing a segment into several equal parts

We use Thales theorem to divide a given line segment into a number of equal parts with compass and straightedge or ruler.  By using a compass and straightedge construction, we do this without measuring the line.

STEPS:

1. Draw the given segment AB. This is the segment that we want to divide.
2. From point A draw an oblique ray (r).
3. Chose a measure with your compass and from point A draw arcs on the oblique ray as many arcs as parts you need.
4. Join the last point of the oblique ray with point B.
5. Draw parallels using your set square to the segment B7 from the other points on the ray.

Here we have divided the segment in seven parts, but you can divide the segment in as many parts as you need.

I think my construction is easier, but here you have another construction. In the applet we divide it into five parts but it can be any number. You will discover that both are the same!.

• Step-by-step construction sheet.
• Try it yourself.

Drawing angles with set squares

Drawing angles with set squares

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Parallel, Perpendicular and Intersecting lines

How do we use the set square?

You have to handle your set square softly and with accuracy without exercising too much pressure on them, only the needed one to avoid movement.

PARALLEL LINES

1. The 45 set square hypotenuse (longest side) is placed attached to the line to which we want to draw the parallels (GUIDE).
2. The 60-30 set square hypotenuse is attached to the 45 set square leg.
3. Fix the 60-30 set square and move the 45 set square upwards or downwards drawing the desired parallel lines along its hypotenuse.

PERPENDICULAR LINES

If we want to draw perpendicular lines to one direction, we will have to follow the first two steps as stated for parallel lines and then the following ones:

1. Having fixed the 60-30 set square, the 45 set square is turned until the other leg is attached to the hypotenuse of the 60-30 set square.
2. Draw the perpendicular line along the hypotenuse of the 45 set square.

Let's review how to draw parallel and perpendicular lines using the triangular set squares.

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