The user-friendly version of this content is available here.
The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.
This essential trains for: SAT-I, GMAT, AMC-8, AMC-10, Math Kangaroo 7-8, Math Kangaroo 9-10.
Most important technique: angle chasing.
When 'chasing angles' it is important to have a puzzle-solver's approach. First of all, determine the value that is easiest to determine. This will reduce the complexity of the problem. In the new problem, determine again the value that is easiest to determine, etc. Repeat this procedure until, eventually, the required angle is found. (Do not focus on the angle you have to find. Focus on the angle you can find.)
Rules for angle chasing:
The interior angles of a plane triangle add up to 180°.
An exterior angle of a triangle is the sum of the two interior angles that are not adjacent to it.
Supplementary angles add up to 180°.
In a right angle triangle, the two acute angles add up to 90°.
When two lines intersect, two pairs of vertical angles are formed (vertical angles are congruent.)
In a circle, an inscribed angle is half the measure of a central angle that is subtended by the same arc.
In a circle, an inscribed angle that is subtended by a diameter has a measure of 90°.
The angle formed by two rays tangent to the same circle is bisected by the line determined by the center of the circle and the intersection of the rays.
The line tangent to a circle forms an angle of 90° with the radius that passes through the point of contact.
Two parallel lines intersected by a secant line form pairs of congruent angles: correspondent, alternate internal, alternate external.
In a cyclic quadrilateral, opposite angles are supplementary.
In a cyclic quadrilateral, congruent angles form a 'butterfly' pattern.