proving congruence
SSS, SAS, AAS, RHS
similar shapes
have the same angles, and proportional sides
for a triangle, if any two sides are proportional and the angle between them is the same, then it is similar (as well as the more obvious conditions)
translations
written as vector - it is easy
rotation (3 details required)
angle of rotation
direction of rotation (clockwise / anticlockwise)
centre of rotation
reflection
need to give equation of mirror line - shapes are congruent under reflection (as well as under translation and rotation)
enlargement (two details)
scale factor (new length / old length)
centre of enlargement
4 key facts about scale factors
if sf > 1: shape gets bigger
sf < 1: shape gets smaller
if sf is negative: shape pops out the other side of enlargement centre (a sf of -1 is just a rotation of 180)
sf tells you the relative distance of old points and new points from centre of enlargement
