12 original questions, 31 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
Using a ruler and compasses only, construct the perpendicular bisector of AB.
You must show all your construction lines.
2 marks
Show answer
Arcs of equal radius (more than 4 cm) drawn from A and from B, crossing above and below AB; the straight line through the two crossing points is the perpendicular bisector, cutting AB at its midpoint at 90 degrees
2
The diagram shows angle ABC.
Using a ruler and compasses only, construct the bisector of angle ABC.
You must show all your construction lines.
Then use a protractor to measure one of the two angles your bisector makes.
2 marks
Show answer
Arc from B crossing both arms, equal arcs from those two points crossing inside the angle, line from B through the crossing; each half measures 38° (accept 36° to 40°)
3
Using a ruler and compasses only, construct an isosceles triangle ABC in which AB = 7 cm and AC = BC = 5 cm.
You must show all your construction arcs.
2 marks
Show answer
Draw AB = 7 cm; arcs of radius 5 cm from A and from B cross at C; joining AC and BC gives the required isosceles triangle
4
Here is a sketch of an equilateral triangle with sides of 6 cm.
Using a ruler and compasses only, construct the triangle accurately in the space below. You must show all your construction arcs.
Write down the size of each angle in your triangle.
2 marks
Show answer
Base 6 cm, arcs of radius 6 cm from each end crossing at the third vertex; each angle is 60°
5
Draw a straight line 10 cm long. Mark a point M on the line, about halfway along.
Using a ruler and compasses only, construct the line perpendicular to the line at the point M.
You must show all your construction lines.
2 marks
Show answer
Equal arcs from M crossing the line either side at X and Y, then larger equal arcs from X and Y crossing above the line; the line through M and that crossing point is perpendicular to the original line at M
6
The diagram shows a line AB.
Using a ruler and compasses only, construct an angle of 60° at A.
You must show all your construction arcs.
2 marks
Show answer
Arc from A crossing AB at X, arc of the same radius from X crossing the first arc; the line from A through that crossing point makes 60° with AB
7
Draw a straight line 10 cm long. Mark a point P about 4 cm above the line.
Using a ruler and compasses only, construct the perpendicular from P to the line.
You must show all your construction lines.
2 marks
Show answer
An arc from P crossing the line at two points, then arcs of equal radius from those two points crossing below the line; the line from P through that crossing point is perpendicular to the original line
8
The diagram shows a straight line with a point A marked on it.
Using a ruler and compasses only, construct an angle of 45° at A.
You must show all your construction lines.
3 marks
Show answer
Construct the perpendicular to the line at A (90°), then bisect the 90° angle; the bisector makes 45° with the line
9
The diagram shows a tree T in a field and a straight fence.
Ellie wants to walk from the tree to the fence by the shortest possible route.
Using a ruler and compasses only, construct the shortest route from T to the fence. You must show all your construction lines.
Explain why this route is the shortest.
3 marks
Show answer
a) open: The perpendicular from T to the fence, found by an arc from T cutting the fence twice and equal arcs from those points crossing on the other sideb) open: The shortest distance from a point to a line is along the perpendicular, which meets the line at 90°
10
Here is a sketch of triangle ABC.
AB = 7 cm, AC = 5 cm and angle BAC = 60°.
Using a ruler and compasses only, construct triangle ABC accurately. You must show all your construction arcs.
3 marks
Show answer
AB = 7 cm drawn, 60° at A constructed with two arcs of equal radius, C marked 5 cm along that line with compasses, then C joined to B
11
Here is a sketch of triangle PQR.
PQ = 8 cm, angle QPR = 45° and angle PQR = 60°.
Using a ruler and compasses only, construct triangle PQR accurately. You must show all your construction lines.
Work out the size of angle PRQ. Check your answer by measuring your drawing.
4 marks
Show answer
a) open: PQ = 8 cm; 45° at P by bisecting a constructed right angle; 60° at Q by two equal arcs; R where the lines crossb) 75°
12
PQRS is a rhombus. Each side of the rhombus is 5 cm long. The diagonal PR is 8 cm long.
Using a ruler and compasses only, construct the rhombus PQRS accurately. You must show all your construction arcs.
Measure the length of the other diagonal, QS.
4 marks
Show answer
a) open: PR = 8 cm drawn; arcs of radius 5 cm from P and from R cross above the line at Q and below at S; join PQ, QR, RS, SPb) 6 cm
Your score
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.