Revision sheet

Constructions

Compass for equal distances, straightedge for lines; justify with congruent triangles.

Watch out: do not change the compass opening between the two arcs.

Translations

$(x, y) \to (x + a, y + b)$; rigid: lengths and angles kept.

Watch out: left and down are negative.

Reflections

$x$-axis: $(x, -y)$; $y$-axis: $(-x, y)$; $y = x$: $(y, x)$.

Watch out: across the $x$-axis, it is $y$ that changes sign.

Rotations about the origin

ccw 90°: $(-y, x)$; 180°: $(-x, -y)$; cw 90°: $(y, -x)$.

Watch out: check the quadrant the image lands in.

Symmetry

Regular $n$-gon: $n$ lines; rotations by $360^\circ/n$.

Watch out: diagonals of a rectangle are not lines of symmetry.

Angle relationships

Vertical: equal. Straight line: 180°. Parallel lines: corresponding/alternate equal, same-side interior 180°. Triangle: 180°.

Watch out: equal or supplementary? Picture the rotation.