There are many ways to show two angles are equal. We usually try the first few techniques listed below, before the last couple.
Using parallel lines;
Using congruent triangles;
Using isosceles triangles;
Using similar triangles;
Circle properties: Angles subtended by the same chord, external angles of cyclic quadrilaterals, alternate segment theorem;
Via a third (or fourth) angle;
Showing the two angles are the sum, difference, twice or half of other equal angles.
. In , , is the foot of the perpendicular from to , is a point on such that and is a point on such that . Show that .
. Let be a parallelogram. Let be a point in the interior of such that . Show that .
. Let the angle bisectors of , , , intersect at . Let be the foot of the perpendicular from to . Show that .
. Let be a quadrilateral such that . Let , be the respective midpoints of and . Extend and to meet at , and to meet at . Show that .