Revision sheet

Dilations

$(x, y) \to (kx, ky)$ about the origin; lengths × $k$, angles kept.

Watch out: multiply, do not add.

Similar figures

Lengths × $k$, perimeters × $k$, areas × $k^2$.

Watch out: scale by multiplying, and square $k$ for areas.

Triangle similarity

AA (or SSS, SAS similarity) → corresponding sides proportional.

Watch out: AA works for triangles only.

Proportional segments

$DE \parallel BC$: $AD/DB = AE/EC$; midsegment = half the third side.

Watch out: keep the parts in matching order.

Similar right triangles

$h^2 = pq$, $a^2 = pc$, $b^2 = qc$; hence $a^2 + b^2 = c^2$.

Watch out: geometric mean, not average.