Exercise 27 Page 47

Let's start by using a ruler to draw the segments.

We are going to attempt to draw a triangle with sides of $4,4$ and $5$ cm. Note that two sides are equal in length which means this would be an isosceles triangle where the equidistant sides make up the triangle's legs and the remaining side is the triangle's base. Let's start by drawing the base of the triangle.

In all isosceles triangles, the legs will join up at the perpendicular bisector of the base. Therefore, to complete the triangle, we have to draw the perpendicular bisector of the base.

Drawing the perpendicular bisector

We can create the perpendicular bisector by drawing two arcs around each endpoint of the base. Two things are important. Make sure that...

1. the compass is opened to more then half the length of the base.
2. you use the same compass setting when drawing both arcs.

The ray that passes through both points of intersection, is the base's perpendicular bisector.

Drawing the triangle

Next we will use a ruler to draw one of the legs. Go up along the perpendicular bisector until the length of the leg is 4 cm.

By connecting the remaining two points, we will have created an isosceles triangle with a base side of $5$ cm and legs of $4$ cm.