Stage 9 - Q1 - 2 marks
On plain paper draw \(AB=5\) cm. Use ruler and compasses to construct an equilateral triangle \(ABC\). State angle \(CAB\).
Hint
The two intersecting arcs must have the same radius as \(AB\).
Stage 9 - Q2 - 2 marks
Two compass arcs of radius 5.5 cm are drawn from A and B, where \(AB\) is also 5.5 cm. Their upper intersection is C. Explain why angle \(CAB\) is exactly \(60^\circ\).
Hint
Use what an arc says about distance from its centre.
Stage 9 - Q3 - 3 marks
On a straight line mark B and C so that \(AB=AC=2\) cm. Construct a perpendicular at A using ruler and compasses.
Hint
The crossing point is equidistant from B and C.
Stage 9 - Q4 - 3 marks
A \(90^\circ\) angle has been constructed with each shown ray at least 2.5 cm long. Bisect it with compasses and state the new angle.
Hint
The second pair of arcs must use equal compass settings.
Stage 9 - Q5 - 4 marks
Construct a \(60^\circ\) angle on a base of 3.5 cm, then bisect it to make \(30^\circ\). Keep all construction arcs.
Hint
Use the equilateral triangle before applying the angle-bisector construction.
Stage 9 - Q6 - 4 marks
Construct a \(60^\circ\) angle on a base of 5.5 cm, then bisect it to make \(30^\circ\). Keep all construction arcs.
Hint
Use the equilateral triangle before applying the angle-bisector construction.
Stage 9 - Q7 - 5 marks
An equilateral triangle has side 5.5 cm. Extend BA through A to D. State and justify angle DAC.
Hint
The extension creates a supplementary angle.
Stage 9 - Q8 - 5 marks
Use a base ray of 6.5 cm. Describe and carry out a ruler-and-compasses construction of \(15^\circ\).
Hint
Two successive bisections divide an angle by four.
Stage 9 - Q9 - 5 marks
Describe an exact ruler-and-compasses route to \(165^\circ\) using \(60^\circ\), \(90^\circ\) and angle bisection. Justify the final angle.
Hint
A supplement and a midpoint between two constructed rays can create new angles.
Stage 9 - Q10 - 3 marks
Using ruler and compasses only, construct \(37.5^\circ\) and then its supplement. Begin from constructed \(60^\circ\) and \(90^\circ\) rays and explain why each result is exact.
Hint
First construct the midpoint direction between the \(60^\circ\) and \(90^\circ\) rays.