Page 128 - MAT KS3 Y8 Cambridge CheckPoint

12.4 Constructing triangles

12.4 Constructing triangles

You already know how to construct some triangles using only a ruler and compasses.
You have used SAS (Side, Angle, Side) and ASA (Angle, Side, Angle).
There are two more types of triangle construction that you still need to learn.
When you know the lengths of all three sides, you can use SSS or Side, Side, Side.

When you know the lengths of the hypotenuse and one other side, you can
use RHS or Right angle, Hypotenuse, Side. You can use just a ruler
and compasses to draw
Worked example 12.4 shows you how to draw these triangles.
these triangles.

Worked example 12.4

Make accurate drawings of these triangles.
a b One is SSS and the other is
5 cm 4 cm 9 cm
RHS.

8 cm 6 cm

a Step 1 Step 2
Draw the base line Open the compasses
8 cm long. to a radius of 5 cm. Put
the point on the left
end of the base line, and
draw an arc above
the base line.
Step 3 Step 4
Change the compasses 5 cm 4 cm Where the two arcs
to a radius of 4 cm. Put cross is the top of the
the point on the right triangle. Join this point
8 cm
end of the base line, to each end of the
and draw an arc above base line. Make sure
the base line, to cross your lines are straight.
the first arc.

b
Step 1 Step 2
Draw a line 12 cm long. Check that the
Draw the perpendicular distance from the
bisector of the line. point of the right
Make this vertical line angle to the end
longer than usual. of the base line is
6 cm exactly 6 cm.

126 12 Constructions