0580

Congruence and Similarity

Lengths, Areas and Volumes

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
  • Enlarging a shape does change its size, so an enlargement is never congruent to the original unless the scale factor is 1
  • To show two shapes are congruent, match up the sides and show 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
Six L-shaped pieces labelled A to F drawn at different sizes and turned to different orientations, so the congruent pairs have to be found by matching measurements rather than by how each one sits on the page
Source: Congruence by Save My Exams
  • Tracing paper settles it quickly on a diagram drawn to scale