Go backwards with roots
From an area ratio, take the square root to get the length ratio; from a volume ratio, take the cube root.
Congruence vs similarity
Congruent = identical (same size and shape: SSS, SAS, ASA, RHS). Similar = same shape, enlarged (equal angles, sides in proportion).
Three scale factors: length, area, volume
If the length scale factor is , the area scale factor is and the volume scale factor is .
Drawn from real examiner reports.
Matching the wrong corresponding sides
Pairing sides that are not in the same position in the two similar shapes.
Identifying corresponding sides in similar triangles was central in examiner reports.
Length SF used for area or volume
Multiplying an area by instead of (or a volume by instead of ).
Enlarging when you should reduce
Going from the larger shape to the smaller one you divide by the scale factor (or use a scale factor below 1). Multiplying instead makes the answer too big.
Using an area ratio as a length ratio
To get the length ratio from areas you must square-root: a length ratio of , not . Using the area ratio directly as the length ratio is a frequent error.
Assuming similar without checking
Two shapes are similar only if all corresponding angles are equal and all corresponding sides are in the same ratio. Do not assume similarity from the look of a diagram alone.
Decide which scale factor first
Write k, then k² for area or k³ for volume, before substituting.
Keep the ratio the same way round
Write each pair of corresponding lengths as new over old (or big over small) and keep that order for every pair, so the scale factor stays consistent throughout.
Justify similarity with equal angles
To show two triangles are similar, state that two pairs of angles are equal (AA), quoting the reason (e.g. same angle, or alternate angles); the third pair then follows.
If corresponding lengths are in the ratio (the length scale factor):
Find corresponding sides by matching equal angles / positions in the two shapes.
Difference between congruent and similar?
Two triangles are similar. A side of cm on the small triangle corresponds to cm on the large one. Another side of the small triangle is cm. Find the corresponding side on the large triangle.
