GCSE Maths Transformations, Congruence and Similarity: lesson and practice questions

By the end of this chapter you will be able to

• Reflect a shape in the lines x = a, y = b, y = x and y = −x, and describe a reflection fully
• Rotate a shape about any centre through 90°, 180° or 270° and describe a rotation fully
• Translate a shape using a column vector and describe a translation
• Enlarge a shape using a positive or fractional scale factor and a centre, and describe an enlargement
• Describe any single transformation fully, and say what changes and what stays the same
• Use the conditions SSS, SAS, ASA and RHS to show that triangles are congruent
• Use scale factors to find missing lengths in similar shapes, and use k, k² and k³ for lengths, areas and volumes

You should already know

• Coordinates in all four quadrants (Chapter 12)
• Angle facts and parallel lines (Chapter 17)
• Ratio and scale factors (Chapter 15)
• Area and volume of simple shapes (Chapters 18 and 19)

Where this leads

• Constructions, loci and vectors (Chapter 22)
• Trigonometry and similar triangles (Chapter 20 links back to this chapter)
• Graph transformations (Chapter 25)
• Circle theorems and proof (Chapter 26)