Congruence (Cambridge International IGCSE Mathematics)

Congruence

What is congruence?

• Two shapes are congruent if they are identical in shape and size

  • One may be a reflection, rotation, or translation of the other

• If one shape is an enlargement of the other, then they are not identical in size and so are not congruent

How do we prove that two shapes are congruent?

• To show that two shapes are congruent you need to show that they are both the same shape and the same size

  • If a shape has been reflected, rotated or translated, then its image is congruent to it

• Show that corresponding sides are the same length

• Show that corresponding angles are the same size

• You do not need to show that they are facing in the same direction

Exam Hint Tracing paper can help in the exam if you are unsure whether two shapes are congruent:

• Trace over one shape and then see if it fits exactly on top of the other
• Only do this if the image is drawn to scale

Worked Example Write down the letters of the two shapes below which are congruent to A*.*

Answer:

Shapes C and D are congruent to A