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 Tip
- 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.
Shapes C and D are congruent to A
