Formulas and computations:
Be able to compute/note down the formulas for if needed:
The relationships between central angle and minor/major arc on p 196, and
additivity of arc measure (be able to fill in angle/arc measures on a circle and give
a brief justification). Most of the computational formulas for these relationships
appear later on; this is just the initial definitions.
Calculating the defect for triangles in hyperbolic geometry (difference of angle
sum from 180). Calculating the area for triangles in hyperbolic geometry (
Finding the equation of a line in hyperbolic geometry (general equation:
x 2 y 2 ax by 1 , use given ( x, y ) pairs to solve for a and b ) .
Finding the length of a segment in hyperbolic geometry: AB* ln( ).
Using the various parallel line transversal theorems to calculate or solve for angle
measures in a "parallel lines + transversal" set up. Plus the triangle sum of angles
theorem for Euclidean geometry.
Computations using the Midpoint Connector Theorems (p 218 for triangles, p 228
for trapezoids) – gives result that a midpoint connector (median) crosses the sides
at the midpoints, is parallel to the base(s), and the formula for the length of the
median of a trapezoid.
Using the proportions set up by the Side-Splitting Theorem to calculate side
lengths in triangles and trapezoids.
The arc/angle relationships in 4.5 (Inscribed Angle Theorem: m A x where
A is an inscribed angle and x is the measure of the intercepted arc, and all the
1 1 1
variant cases on p272: m A ( x y), m A ( x y), m A x (tangent) )
2 2 2
Two-Chord Theorem: AP PB CP PD .
Secant-Tangent Theorem: PC 2 PA PB .
Two-Secant Theorem: PA PB PC PD . For the previous three, be sure you
know what segments those refer to (make sketches)
Areas of basic plane figures (on formula sheet); combining into more complex
Using similar triangles to set up proportions and solve for side lengths.
Volumes and surface areas of basic solids. You do not need to know the formulas
for the Platonic solids.
Length of arc L r and area of sector A r 2 .
Law of sines and law of cosines.
How find a vector given coordinate points. Addition of vectors. Finding x and y
components of vectors given magnitude and angle, and vice versa. Calculating the
length (norm, magnitude) of a vector, and finding a unit vector.
Using direction cosines to find the angle that a vector in 3D makes with x, y, and
Dot product formula ( u v u1v1 u2v2 u3v3 ), and formula for finding angle
between two vectors ( cos 1 ( ) ).
|| u || || v ||
How to normalize a vector ( u ) and find a vector in the direction of a given
|| v ||
vector ( || w || gives a vector in the direction of v having the length of w ).
|| v ||
Euclidean regular polygon computations:
o Sum of vertex angles: 180(n 2) , measure of each angle that sum divided
by n .
o Measure of central angle always
o Apothem: .5s cot , where is half the measure of the central angle, s is
o Perimeter: ns
o Area: .5asn
Non-Euclidean polygon computations:
o Difference between actual angle sum and Euclidean sum is defect
o Area computed from