Maths · Topic 2: Year 11
Similarity and congruence
Congruent triangles and geometric proof, similar shapes and scale factors, similar triangles with parallel lines, and how area and volume scale in similar 2D and 3D shapes.
Lessons
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1
Congruence
Recognise congruent shapes, use the four conditions for congruent triangles, and use congruence to find missing lengths and angles.
6 terms -
2
Geometric proof and congruence
Write clear geometric proofs, using congruent triangles to prove properties of shapes such as isosceles triangles and parallelograms.
6 terms -
3
Similarity
Recognise similar shapes, find scale factors and missing lengths, and use equal angles to show triangles are similar.
6 terms -
4
More similarity
Use similar triangles formed by parallel lines, and use the fact that areas of similar shapes scale by the square of the length scale factor.
6 terms -
5
Similarity in 3D solids
Use length, area and volume scale factors for similar solids, including cones, cylinders and frustums.
6 terms
Downloads
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- Congruence.pptx Built from the lesson script on 30 September 2026. View
- Congruence - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Congruence - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Geometric proof and congruence.pptx Built from the lesson script on 30 September 2026. View
- Geometric proof and congruence - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Geometric proof and congruence - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Similarity.pptx Built from the lesson script on 30 September 2026. View
- Similarity - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Similarity - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- More similarity.pptx Built from the lesson script on 30 September 2026. View
- More similarity - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- More similarity - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Similarity in 3D solids.pptx Built from the lesson script on 30 September 2026. View
- Similarity in 3D solids - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Similarity in 3D solids - Exam Questions.docx Built from the lesson script on 30 September 2026. View
Key terms in this chapter
All 30, gathered from every lesson.
- 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.
- Proof
- A logical argument showing a statement is always true.
- Statement
- A fact written in a proof.
- Reason
- The rule that justifies a statement.
- Corresponding
- In matching positions in congruent triangles.
- Common side
- A side shared by two triangles.
- Bisect
- Cut exactly in half.
- Similar
- The same shape but a different size.
- Scale factor
- The multiplier that takes one length to the corresponding length.
- Corresponding sides
- Sides in matching positions.
- Ratio
- A comparison of two quantities.
- Enlargement
- A transformation that produces similar shapes.
- Equiangular
- Having equal angles.
- Similar triangles
- Triangles with equal angles and proportional sides.
- Scale factor
- The multiplier for lengths.
- Area scale factor
- The square of the length scale factor.
- Parallel
- Lines that never meet.
- Corresponding angles
- Equal angles in matching positions on parallel lines.
- Ratio
- A comparison of two quantities.
- Similar solids
- Solids with the same shape and all lengths in the same ratio.
- Volume scale factor
- \(k^3\).
- Surface area scale factor
- \(k^2\).
- Frustum
- A cone or pyramid with the top cut off parallel to the base.
- Capacity
- The volume a container holds.
- Density
- Mass per unit volume; the same in similar solids of the same material.