Rukasha Maths

GCSE maths Beta

Transformations, similarity and congruence · Revision guide

Foundation · Geometry · 3 pages in the PDF

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Learning objectives

  • Describe and perform a transformation completely.
  • Distinguish similarity from congruence.

Key ideas

A translation specifies horizontal and vertical movements, often as a column vector.

A reflection needs a mirror line; a rotation needs a centre, angle and direction.

An enlargement needs a centre and scale factor. For a positive factor, multiply distances from the centre.

Similar figures have equal corresponding angles and a common corresponding length ratio.

Congruent figures have equal corresponding lengths and angles. Use a valid triangle congruence test.

SSS, SAS, ASA, RHS\text{SSS, SAS, ASA, RHS}

Worked examples

Example 1

Enlarge the point about the origin by the given positive factor.

A=(2,3),O=(0,0),k=2A=(2,3),\quad O=(0,0),\quad k=2

Multiply both distances from the origin.

A′=(2×2, 2×3)=(4,6)A'=(2\times2,\ 2\times3)=(4,6)
A′=(4,6)A'=(4,6)

Example 2

Reflect the point in the vertical axis.

Reverse the horizontal coordinate; keep the vertical coordinate.

(3,−2) →reflection in y-axis (−3,−2)(3,-2)\ \xrightarrow{\text{reflection in }y\text{-axis}}\ (-3,-2)
(−3,−2)(-3,-2)

Watch out

Equal corresponding angles establish triangle similarity, not congruence. An enlargement acts on distances from its centre.