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Congruence - 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
Congruence
Similarity and congruence
Lesson 1 of 5
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up
Similarity and congruence
Lesson 1 of 5
Answer each one, then check.
1
What do the angles in a triangle add up to?
2
What does isosceles mean?
3
What is a right-angled triangle's longest side called?
4
Do reflections keep the size of a shape?
5
What do the angles on a straight line add up to?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up - Answers
Similarity and congruence
Lesson 1 of 5
1
What do the angles in a triangle add up to?
180°
2
What does isosceles mean?
Two equal sides
3
What is a right-angled triangle's longest side called?
The hypotenuse
4
Do reflections keep the size of a shape?
Yes
5
What do the angles on a straight line add up to?
180°
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Similarity and congruence
Lesson 1 of 5
1
Explain what congruent means.
2
Use SSS, SAS, ASA and RHS to show triangles are congruent.
3
Explain why AAA and SSA do not prove congruence.
4
Use congruence to find missing sides and angles.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Similarity and congruence
Lesson 1 of 5
CONGRUENT
Two shapes are congruent if they are exactly the same shape and size.
One can be moved onto the other by a rotation, a reflection, a translation, or a combination.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
The Four Congruence Conditions
Similarity and congruence
Lesson 1 of 5
If two triangles satisfy any one of these, they are congruent.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
The Four Conditions
Similarity and congruence
Lesson 1 of 5
Learn the letters and what they mean.
Condition
Means
Example
SSS
All three sides equal
5, 6, 7 and 5, 6, 7
SAS
Two sides and the included angle equal
5, 40°, 7 and 5, 40°, 7
ASA
Two angles and a corresponding side equal
50°, 6, 70°
RHS
Right angle, hypotenuse and one other side equal
Right angle, 10, 6
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Proving Two Triangles Congruent
Similarity and congruence
Lesson 1 of 5
Triangle ABC has AB = 5 cm, BC = 7 cm and angle ABC = 50°. Triangle PQR has PQ = 5 cm, QR = 7 cm and angle PQR = 50°. Are the triangles congruent?
1
Two pairs of equal sides
AB = PQ and BC = QR
2
The angle between them is equal too
Angle B = angle Q = 50°
3
Two sides and the included angle
SAS
ANSWER
Yes, the triangles are congruent by SAS.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Conditions That Do NOT Work
Similarity and congruence
Lesson 1 of 5
AAA
Three equal angles give similar triangles, but they can be different sizes.
SSA
Two sides and a non-included angle can give two different triangles.
Only sides
Two sides alone are not enough.
Angles not between the sides
If the angle is not between the two sides, it is not SAS.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Using Congruence to Find a Length
Similarity and congruence
Lesson 1 of 5
Triangles ABC and DEF are congruent by SSS, with A matching D, B matching E and C matching F. AB = 6 cm, BC = 8 cm, DF = 10 cm. Find AC and DE.
1
Corresponding sides are equal
AB = DE, BC = EF, AC = DF
2
Find AC
AC = DF = 10 cm
3
Find DE
DE = AB = 6 cm
ANSWER
AC = 10 cm and DE = 6 cm.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Writing the Reason
Similarity and congruence
Lesson 1 of 5
A congruence answer needs three things.
The equal parts
Write which sides or angles are equal, with the reason for each.
The condition
State SSS, SAS, ASA or RHS.
The conclusion
"So triangle ABC is congruent to triangle DEF."
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Similarity and congruence
Lesson 1 of 5
Congruent
Exactly the same shape and size.
Corresponding
In matching positions in two shapes.
Included angle
The angle between two given sides.
Hypotenuse
The longest side of a right-angled triangle.
SSS, SAS, ASA, RHS
The four conditions for congruent triangles.
Similar
The same shape but a different size.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Similarity and congruence
Lesson 1 of 5
YOUR TASK
Congruent or Not?
12 minutes
Decide which pairs of triangles are congruent and name the condition. (a) 4, 5, 6 and 6, 4, 5 (b) sides 5 and 8 with an angle of 30° between them, and sides 5 and 8 with an angle of 40° between them (c) angles 40°, 60°, 80° in both triangles, but one has a side of 3 cm and the other a side of 6 cm.
1
Match the equal parts.
2
Name the condition.
WHAT A GOOD ANSWER SHOWS
(a) Congruent by SSS. (b) Not congruent: the included angles differ. (c) Not congruent: AAA does not prove congruence; the sides are different sizes, so the triangles are similar.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Similarity and congruence
Lesson 1 of 5
Say what congruent means.
Recall SSS, SAS, ASA and RHS.
Decide whether two triangles are congruent.
Explain why AAA is not enough.
Explain why SSA is not enough.
Find corresponding sides and angles.
Use congruence to find a length.
Write a clear reason.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Congruent means identical in shape and size.
Conditions: SSS, SAS, ASA (or AAS), RHS.
AAA and SSA do not prove congruence.
Always give the condition as your reason.
EXAM FOCUS
Triangle ABC has AB = 6 cm, AC = 8 cm and angle A = 50°. Triangle PQR has PQ = 6 cm, PR = 8 cm and angle P = 50°. Show that the two triangles are congruent. (3 marks)
Name the pairs of equal parts and check the angle is between the two sides. Then state SAS.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Congruence
Similarity and congruence
Lesson 1 of 5
Answer all questions. Give reasons for your answers. · 25 minutes
Question 1 · 3 marks · Give a reason
The diagram shows three triangles A, B and C. Two of the triangles are congruent. Write down which two, and give a reason.
Question 2 · 3 marks · Show that
Triangle ABC has AB = 5 cm, BC = 7 cm and angle ABC = 50°. Triangle PQR has PQ = 5 cm, QR = 7 cm and angle PQR = 50°. Show that triangle…
Question 3 · 2 marks · Give a reason
Two triangles both have angles of 40°, 60° and 80°. Ben says they must be congruent. Explain why Ben is not necessarily correct.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Congruence (cont.)
Similarity and congruence
Lesson 1 of 5
Question 4 · 2 marks · Work out
Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 6 cm, BC = 8 cm and DF = 10 cm. Write down the…
Question 5 · 3 marks · Explain
Triangle ABC is right-angled at B, with hypotenuse AC = 10 cm and AB = 6 cm. Triangle PQR is right-angled at Q, with hypotenuse PR = 10 cm…
Question 6 · 2 marks · Decide
Triangle ABC has sides 4 cm, 5 cm and 6 cm. Triangle DEF has sides 6 cm, 4 cm and 5 cm. Are the triangles congruent? Give a reason.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · 3 marks · Give a reason
Similarity and congruence
Lesson 1 of 5
The diagram shows three triangles A, B and C. Two of the triangles are congruent. Write down which two, and give a reason. (3 marks)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · mark scheme
Similarity and congruence
Lesson 1 of 5
3 marks available. Award a mark for each point made.
A and B
B1
Two sides and the included angle equal
M1
SAS
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · 3 marks · Show that
Similarity and congruence
Lesson 1 of 5
“
Triangle ABC has AB = 5 cm, BC = 7 cm and angle ABC = 50°. Triangle PQR has PQ = 5 cm, QR = 7 cm and angle PQR = 50°. Show that triangle ABC is congruent to triangle PQR.
HOW TO ANSWER IT
Command word: Show that. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · mark scheme
Similarity and congruence
Lesson 1 of 5
3 marks available. Award a mark for each point made.
Equal sides stated
M1
Equal included angle stated
M1
SAS and conclusion
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · 2 marks · Give a reason
Similarity and congruence
Lesson 1 of 5
“
Two triangles both have angles of 40°, 60° and 80°. Ben says they must be congruent. Explain why Ben is not necessarily correct.
HOW TO ANSWER IT
Command word: Give a reason. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · mark scheme
Similarity and congruence
Lesson 1 of 5
2 marks available. Award a mark for each point made.
AAA is not a congruence condition
M1
The triangles could be different sizes
C1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · 2 marks · Work out
Similarity and congruence
Lesson 1 of 5
“
Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 6 cm, BC = 8 cm and DF = 10 cm. Write down the length of AC.
HOW TO ANSWER IT
Command word: Work out. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · mark scheme
Similarity and congruence
Lesson 1 of 5
2 marks available. Award a mark for each point made.
Corresponding sides identified
M1
10
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · 3 marks · Explain
Similarity and congruence
Lesson 1 of 5
“
Triangle ABC is right-angled at B, with hypotenuse AC = 10 cm and AB = 6 cm. Triangle PQR is right-angled at Q, with hypotenuse PR = 10 cm and PQ = 6 cm. Explain why the triangles are congruent.
HOW TO ANSWER IT
Command word: Explain. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · mark scheme
Similarity and congruence
Lesson 1 of 5
3 marks available. Award a mark for each point made.
Right angle in each
B1
Hypotenuse and one other side equal
M1
RHS
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · 2 marks · Decide
Similarity and congruence
Lesson 1 of 5
“
Triangle ABC has sides 4 cm, 5 cm and 6 cm. Triangle DEF has sides 6 cm, 4 cm and 5 cm. Are the triangles congruent? Give a reason.
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
Similarity and congruence
Lesson 1 of 5
2 marks available. Award a mark for each point made.
Yes
B1
SSS
B1
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