Construct triangle ABC: AB = 7 cm, BC = 5 cm, AC = 6 cm Easy

The question

Question: construct triangle A B C with A B = 7 cm, B C = 5 cm and A C = 6 cm, using a ruler and compasses.

We only use a ruler for straight lines and a pair of compasses for arcs.

The arcs stay on the paper.

1 Draw the base

With the ruler, draw A B, 7 cm long.

2 Arc from A

Open the compass to A C, 6 cm.

Put the point on A and draw an arc where C will be.

Careful!

Leave the arcs on the paper.

They show how the triangle was made.

3 Arc from B

Open the compass to B C, 5 cm.

From B, draw an arc.

The two arcs cross at C.

4 Join

With the ruler, join A to C and B to C.

5 Check

Let's check with the ruler: A C is 6 cm and B C is 5 cm, as asked.

So the triangle is right!

Let's look back.

First: draw the base.

Then: arc from A.

Then: arc from B.

Then: join.

Last: check.

▶ Watch it solved

Construct the perpendicular bisector of AB = 8 cm Medium

The question

Question: construct the perpendicular bisector of a line A B, 8 cm long.

The perpendicular bisector cuts A B in half, at a right angle.

1 Draw AB

Draw A B, 8 cm long.

2 Arcs from A

Open the compass to more than half of A B: 5 cm.

From A, draw an arc above and an arc below.

Careful!

Do not change the compass.

The arcs from B must have the same opening as the arcs from A.

3 Arcs from B

Keep the same opening.

From B, draw two arcs.

They cross the first arcs at P and Q.

4 Join the crossings

With a ruler, join P and Q.

This line cuts A B in half at M, at a right angle: the perpendicular bisector.

5 Check

Let's check: A M and M B are both 4 cm, and the angle at M is 90°.

So it is right!

Let's look back.

First: draw AB.

Then: arcs from A.

Then: arcs from B.

Then: join the crossings.

Last: check.

▶ Watch it solved

Construct the bisector of an angle of 70° Harder

The question

Question: construct the bisector of an angle of 70°.

1 Draw the angle

Draw the two lines meeting at V, with 70° between them.

2 Arc from the corner

From the corner V, draw an arc that cuts both lines, at P and Q.

3 Arcs from P and Q

With the same opening from P and from Q, draw two arcs.

They cross at R.

Careful!

Keep the compass the same for both arcs.

Then R is the same distance from both lines.

4 Join V and R

Join V to R with a ruler, and go on.

This line cuts the angle in half: 35° and 35°.

5 Check

Let's check with a protractor: both halves are 35°.

So it is right!

Let's look back.

First: draw the angle.

Then: arc from the corner.

Then: arcs from P and Q.

Then: join V and R.

Last: check.

▶ Watch it solved