Identify, describe and construct congruent and similar shapes, including…

The idea

This topic covers identifying, describing and constructing congruent and similar shapes using the four transformations: rotation, reflection, translation and enlargement. Congruent shapes are identical in shape and size, so rotation, reflection and translation produce congruent images; enlargement produces a similar shape On coordinate axes you track vertex coordinates through each transformation. For a rotation, give the centre, angle and direction; for a reflection, give the mirror line; for a translation, give the column vector; for an enlargement, give the centre and scale factor. To construct an image, transform each vertex and join them in order. Describing a transformation means stating all required details so the mapping is unambiguous.

What earns the marks

• Identify congruent shapes as identical in shape and size, and similar shapes as having equal corresponding angles with sides in the same ratio.
• Describe a rotation fully by giving the centre of rotation, the angle and the direction (clockwise or anticlockwise).
• Describe a reflection by giving the equation of the mirror line, such as x = 2 or y = x.
• Describe a translation by giving the column vector, for example (3 over −2), and apply it to each vertex.
• Describe an enlargement by giving the centre of enlargement and the scale factor where required.
• Construct images on coordinate axes by transforming each vertex accurately and joining corresponding vertices in the correct order.

Common mistakes and how to put them right

• Describing a rotation without stating the centre, angle or direction.

  Put it right by giving all three pieces of information.

• Confusing reflection and rotation when the image looks similar.

  Put it right by checking whether the orientation is reversed (reflection) or turned (rotation).

• Applying a translation to only one vertex.

  Put it right by applying the same column vector to every vertex of the shape.

Exam tips

• Use tracing paper or count squares from the centre to check rotations and enlargements before finalising your answer.
• For descriptions, write the transformation name first, then list every required detail in a clear order.
• When constructing on coordinate axes, label the image vertices with primes (A′, B′, C′) to avoid confusion with the original.
• Check that corresponding sides remain in the same ratio for similarity, and that lengths are unchanged for congruence.