Three scale factors: length, area, volume
If the length scale factor is , the area scale factor is and the volume scale factor is .
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 (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), RHS (Right angle-Hypotenuse-Side). Similar = same shape, enlarged (equal angles, sides in proportion).
Drawn from real examiner reports.
Using the length scale factor for area or volume
Multiplying an area by instead of (or a volume by instead of ).
Matching the wrong corresponding sides
Pairing sides that are not in the same position in the two similar shapes.
Decide which scale factor first
Write k, then k² for area or k³ for volume, before substituting.
If corresponding lengths are in the ratio (the length scale factor):
Find corresponding sides by matching equal angles / positions in the two shapes.
Similar vs congruent — what is the difference in one line each?
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.
