The set square slides

The idea

Align a ruler with the base, place a set square on it with one edge of the right angle along the ruler, slide it until the vertical edge touches the vertex, and draw the altitude along that edge.

Drawing a right angle on paper

You must draw the altitude from A to BC on paper. You have a ruler and a set square. A set square has a right angle in one corner.

How can the set square help you?

• Its right-angle edge can slide along the ruler up to A
• Its slanting edge measures the angle
• It cannot help, only a protractor can

Slide the set square

Follow the steps: ruler along the base, set square on the ruler, slide it to A, draw. Then try a second triangle.

Ruler, set square, slide, draw

The set square has two edges at a right angle. One edge rests on the ruler. The other, the upright edge, is then at 90° to the ruler.

The ruler lies along BC, so the line drawn along the upright edge is at 90° to BC. That is the altitude. If the foot is outside the triangle, extend BC along the ruler.

To draw an altitude: put a ruler along the base, rest one edge of a set square’s right angle on it, slide the set square until its upright edge touches the vertex, and draw along that edge. The line is at 90° to the base.

• Step | What to do
• 1 | Put the ruler along the base BC.
• 2 | Put the set square on the ruler, with one edge of its right angle along the ruler.
• 3 | Slide it along the ruler until the upright edge touches A.
• 4 | Draw along the upright edge from A to the base line.

Notes

To draw an altitude: put a ruler along the base, rest one edge of a set square’s right angle on it, slide the set square until its upright edge touches the vertex, and draw along that edge. The line is at 90° to the base.

Check yourself

Which edge of the set square do you draw along to make the altitude?

The upright edge of the set square and the ruler make a right angle. How many degrees is it?

Answer: 90

The corner of a set square is a right angle: 90°. That is why the upright edge is at 90° to the ruler.

The triangle has an obtuse angle at B, so the corner A is far to the left of B. After you slide the set square onto A, what must you do with the base BC?

Why is the line drawn along the upright edge at 90° to BC?

• The edge that rests on the ruler. That edge lies along BC. Drawing along it would only draw BC again.
• The slanting edge. The slanting edge is not at 90° to the ruler. Only the upright edge of the right angle gives the altitude.
• The upright edge, the one at 90° to the edge on the ruler — correct. Yes! The upright edge is at 90° to the ruler, and so to BC.
• Nothing. The altitude meets BC inside the triangle. With an obtuse angle at B the foot falls outside BC. The ruler line has to be extended.
• Move the corner A to the right. You must not move the corner. The altitude is for this triangle, so extend BC instead.
• Extend BC along the ruler, so that the upright edge has a base line to meet — correct. Yes! The foot of the altitude is outside the triangle, on the extension of BC.
• Because the ruler is straight. A straight ruler only keeps the base line straight. The 90° comes from the set square.
• The edge on the ruler lies along BC, and the two edges of the set square meet at 90° — correct. Yes! The right angle of the set square is carried along the ruler.
• Because the set square is flat. Every set square is flat. The 90° comes from its right angle.