Angle rules and similarity tests
Vertically opposite angles are equal. Adjacent angles on a straight line add to 180°. Parallel lines give equal corresponding angles, equal alternate angles and co-interior angles adding to 180°.
Similar triangles have the same shape, but need not have the same size or orientation. AAA: all three pairs of corresponding angles match. If two pairs are given equal, derive the third in each triangle using 180° minus the two known angles. SAS: two pairs of sides in the same ratio with equal included angles. SSS: all three pairs of corresponding sides in the same ratio. A single matching angle alone is not enough.
Original classroom questions. Use the labelled information and markings, not measurements from the drawing. You can revisit any question; showing a solution does not mark it complete.