Congruence and Similarity

Same shape, same size

• Two shapes are congruent when neither their form nor their measurements differ in any way
• Turning one round, flipping it over or sliding it somewhere else leaves it congruent, since a rotation, a reflection and a translation all move a shape without resizing it
• An enlargement changes a shape's size unless its scale factor is 1 or −1, so those are the only enlargements whose image is congruent to the original (a scale factor of −1 turns the shape through 180°)
• To decide whether two shapes are congruent, match up the sides and check that corresponding lengths are equal, then do the same for the angles
• The two shapes need not face the same way, so match corresponding parts rather than comparing them where they sit

• Tracing paper settles it quickly on a diagram drawn to scale