Page 129 - MAT KS3 Y8 Cambridge CheckPoint

12.4 Constructing triangles

Step 3 Step 4
Open the compasses to a Where the arc crosses
radius of 9 cm. Put the vertical line is the
9 cm
the point on the right- top of the triangle.
hand end of the base Join this point with
line. Draw an arc that a straight line to the
meets the vertical line. right-hand end of the
6 cm 6 cm
base line.

✦ Exercise 12.4

1 a Draw an accurate copy of triangle ABC. A
b Measure and write down the size of angle: 65 mm 75 mm
i ABC ii BAC iii ACB.
B 95 mm C
c Add together the three answers you gave in part b.
d Explain how you can use your answer to part c to check that you have
measured the angles in the triangle accurately.
2 a Draw an accurate copy of triangle DEF. D
b Measure and write down the length of the side DF.
c Measure and write down the size of angle: 86 mm
i DEF ii EDF
d What type of triangle is DEF? Explain your answer.
E 61 mm F
3 Sasha and Dakarai both sketch a triangle XYZ. Read what Sasha says.

If we draw these triangles accurately, I think that angle XZY in
my triangle will be smaller than angle XZY in your triangle.

a
s
s
tch
ke
ra
ka
’
i
e
Sasha’s sketch Dakarai’s sketch
D
tch
Is Sasha correct? Show how you worked out your answer.
Summary

You should now know that: You should be able to:
★ The midpoint of a line segment AB is the point ★ Use a ruler and compasses to construct circles
that is exactly halfway between A and B. and arcs.
★ The perpendicular bisector of a line segment AB is ★ Use a straight-edge and compasses to construct
the line that passes through the midpoint of AB at the midpoint and perpendicular bisector of a line
right angles to AB. segment and the bisector of an angle.
★ The angle bisector of angle ABC is the line that ★ Use a ruler and compasses to construct a triangle,
cuts the angle exactly in half. given three sides (SSS) and given a right angle,
hypotenuse and one side (RHS).

12 Constructions 127