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Constructions 1 - Teacher Slides.pptx
The lesson slides with the teacher's notes on each slide, and every question and mark scheme built in. Built from the lesson script on 30 September 2026.
EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Constructions 1
Transformations and constructions
Lesson 6 of 8
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up
Transformations and constructions
Lesson 6 of 8
Answer each one, then check.
1
What do the angles in a triangle add up to?
2
What is a perpendicular line?
3
What does bisect mean?
4
What is the longest side of a right-angled triangle called?
5
What is the midpoint of a line 8 cm long?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up - Answers
Transformations and constructions
Lesson 6 of 8
1
What do the angles in a triangle add up to?
180°
2
What is a perpendicular line?
One that meets another at 90°
3
What does bisect mean?
Cut exactly in half
4
What is the longest side of a right-angled triangle called?
The hypotenuse
5
What is the midpoint of a line 8 cm long?
The point 4 cm from each end
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Transformations and constructions
Lesson 6 of 8
1
Construct a triangle given three sides (SSS).
2
Construct a triangle given two sides and the angle between them (SAS).
3
Construct the perpendicular bisector of a line segment.
4
Explain why a triangle can or cannot be constructed.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
The Rules of Construction
Transformations and constructions
Lesson 6 of 8
Use only a pencil, a ruler for straight lines, and compasses.
Keep the construction arcs
Do not rub them out: they show your method and earn marks.
Sharp pencil
Thin lines make the intersections easy to see.
Keep the compasses fixed
Do not change the radius between two arcs that must be equal.
Label the lengths
Write the length beside each side, and mark any angles.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Constructing a Triangle from Three Sides
Transformations and constructions
Lesson 6 of 8
The point where the two arcs cross is the third vertex.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Constructing an SSS Triangle
Transformations and constructions
Lesson 6 of 8
For a triangle with sides 6 cm, 5 cm and 4 cm.
1
Draw the longest side
Measure 6 cm with a ruler and label the ends A and B.
2
Set the compasses to 5 cm
Put the point at A and draw an arc above the line.
3
Set the compasses to 4 cm
Put the point at B and draw a second arc crossing the first.
4
Mark C where the arcs cross
Join C to A and C to B with a ruler.
5
Label and check
Measure to check each side and keep the arcs.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can the Triangle Be Made?
Transformations and constructions
Lesson 6 of 8
Can a triangle be constructed with sides 3 cm, 4 cm and 8 cm?
1
The two shorter sides must add up to more than the longest
3 + 4 = 7
2
Compare with the longest side
7 < 8
3
The arcs would not meet
The two short sides cannot reach each other
ANSWER
No: 3 + 4 < 8, so the arcs do not cross and no triangle exists.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
An SAS Triangle
Transformations and constructions
Lesson 6 of 8
Construct a triangle with sides of 5 cm and 7 cm and an angle of 40° between them.
1
Draw the 7 cm side
Label the ends A and B
2
Measure 40° at A
Use a protractor and mark the angle
3
Draw a line from A through the mark
Measure 5 cm along it and label C
4
Join B to C
The triangle ABC is complete
ANSWER
Triangle ABC with AB = 7 cm, AC = 5 cm and angle A = 40°.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
The Perpendicular Bisector
Transformations and constructions
Lesson 6 of 8
Every point on the perpendicular bisector is the same distance from A and B.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Constructing the Perpendicular Bisector
Transformations and constructions
Lesson 6 of 8
The same radius from both ends.
1
Open the compasses more than half of AB
Any radius bigger than half will do
2
Draw arcs from A above and below the line
Keep the same radius
3
Draw arcs from B, crossing the first arcs
Do not change the radius
4
Mark the two crossing points
One above and one below AB
5
Join the crossing points with a ruler
This line bisects AB at 90°
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Which Construction?
Transformations and constructions
Lesson 6 of 8
SSS TRIANGLE
• You know all three sides.
• Use two arcs to find the third vertex.
• Always check the two shorter sides add to more than the longest.
SAS TRIANGLE
• You know two sides and the angle between them.
• Use a protractor for the angle.
• The third side is found by joining the ends.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Transformations and constructions
Lesson 6 of 8
Construct
Draw accurately using only a ruler and compasses (a protractor when an angle is given).
Compasses
An instrument for drawing arcs and circles.
Arc
Part of the circumference of a circle.
Bisect
To cut exactly in half.
Perpendicular bisector
A line at 90° through the midpoint of a segment.
Vertex
A corner of a shape.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Transformations and constructions
Lesson 6 of 8
YOUR TASK
Construct and Measure
15 minutes
Construct a triangle with sides 7 cm, 6 cm and 5 cm. Measure the three angles with a protractor and add them up. Then construct the perpendicular bisector of the 7 cm side and check it passes through the opposite vertex or not.
1
Construct with compasses.
2
Measure the angles.
3
Check the sum.
WHAT A GOOD ANSWER SHOWS
The angles are about 78°, 57° and 44° (sum 180°). The perpendicular bisector of the 7 cm side does not pass through the opposite vertex because the triangle is scalene; it would only do that for an isosceles triangle with equal sides on either side.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Transformations and constructions
Lesson 6 of 8
Draw a line of exact length.
Construct an SSS triangle.
Construct an SAS triangle.
Use a protractor accurately.
Construct a perpendicular bisector.
Keep construction arcs.
Test whether three lengths make a triangle.
Explain each step of a construction.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
SSS: draw the longest side, then two arcs.
SAS: draw one side, measure the angle, then measure the second side.
The perpendicular bisector cuts a segment in half at 90°.
Always leave your construction lines.
EXAM FOCUS
Using ruler and compasses only, construct the perpendicular bisector of the line AB. You must show all your construction lines. (2 marks)
Use the same compass setting from both ends, more than half of AB. Do not rub out the arcs.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Constructions 1
Transformations and constructions
Lesson 6 of 8
Answer all questions. Use a sharp pencil, a ruler, compasses and a protractor. Show all construction lines. · 30 minutes
Question 1 · 3 marks · Construct
Using ruler and compasses only, construct a triangle with sides of length 6 cm, 5 cm and 4 cm. Show all your construction lines.
Question 2 · 2 marks · Construct
The line AB is 6 cm long. Using ruler and compasses only, construct the perpendicular bisector of the line AB. Show all your construction…
Question 3 · 2 marks · Explain
Explain why it is not possible to construct a triangle with sides of length 3 cm, 4 cm and 8 cm.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Constructions 1 (cont.)
Transformations and constructions
Lesson 6 of 8
Question 4 · 3 marks · Construct
Construct a triangle ABC with AB = 7 cm, AC = 5 cm and angle BAC = 40°.
Question 5 · 2 marks · Measure
In the triangle with sides 6 cm, 5 cm and 4 cm, measure the size of the largest angle.
Question 6 · 2 marks · Decide
For each set of lengths, state whether a triangle can be constructed. (a) 5 cm, 6 cm, 7 cm (b) 2 cm, 3 cm, 6 cm
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · 3 marks · Construct
Transformations and constructions
Lesson 6 of 8
“
Using ruler and compasses only, construct a triangle with sides of length 6 cm, 5 cm and 4 cm. Show all your construction lines.
HOW TO ANSWER IT
Command word: Construct. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · mark scheme
Transformations and constructions
Lesson 6 of 8
3 marks available. Award a mark for each point made.
A 6 cm line drawn accurately
B1
Both arcs drawn correctly
M1
Triangle completed and arcs shown
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · 2 marks · Construct
Transformations and constructions
Lesson 6 of 8
The line AB is 6 cm long. Using ruler and compasses only, construct the perpendicular bisector of the line AB. Show all your construction lines. (2 marks)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · mark scheme
Transformations and constructions
Lesson 6 of 8
2 marks available. Award a mark for each point made.
Arcs of equal radius from A and B
M1
Correct crossings, both sides
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · 2 marks · Explain
Transformations and constructions
Lesson 6 of 8
“
Explain why it is not possible to construct a triangle with sides of length 3 cm, 4 cm and 8 cm.
HOW TO ANSWER IT
Command word: Explain. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · mark scheme
Transformations and constructions
Lesson 6 of 8
2 marks available. Award a mark for each point made.
3 + 4 = 7
M1
7 < 8, so the arcs do not meet
C1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · 3 marks · Construct
Transformations and constructions
Lesson 6 of 8
“
Construct a triangle ABC with AB = 7 cm, AC = 5 cm and angle BAC = 40°.
HOW TO ANSWER IT
Command word: Construct. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · mark scheme
Transformations and constructions
Lesson 6 of 8
3 marks available. Award a mark for each point made.
AB drawn accurately
B1
Angle of 40° at A
M1
AC = 5 cm and triangle completed
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · 2 marks · Measure
Transformations and constructions
Lesson 6 of 8
“
In the triangle with sides 6 cm, 5 cm and 4 cm, measure the size of the largest angle.
HOW TO ANSWER IT
Command word: Measure. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · mark scheme
Transformations and constructions
Lesson 6 of 8
2 marks available. Award a mark for each point made.
Identifying the angle opposite the 6 cm side
M1
83 (within the range)
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · 2 marks · Decide
Transformations and constructions
Lesson 6 of 8
“
For each set of lengths, state whether a triangle can be constructed. (a) 5 cm, 6 cm, 7 cm (b) 2 cm, 3 cm, 6 cm
HOW TO ANSWER IT
Command word: Decide. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · mark scheme
Transformations and constructions
Lesson 6 of 8
2 marks available. Award a mark for each point made.
(a) Yes
B1
(b) No
B1
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