Geometry references
References 
circle 
A=pir^{2}; C=2pir: 2pi=360 
rectangular 
A=lw 
trangle 
A=1/2bh 

c^{2}=a^{2}+b^{2}; 345,51213 

ssssqrt(2); xxsqrt(3)2x; 180=sum 
rectangular prism 
V=lwh; sa=2(lw +lh+hw) 
cyclinder 
V=pi*r^{2}h; sa=2pi rh +pirr 
cone 
V=pi*r^{2}h/3 
triangular prism 
V=lwh/3 
sphere 
V=4pi*r^{3}/3; sa=4pirr 
Line and angles
LINEs and ANGLES 
line,ray,line segment 
0,1,2 ends 
supplementary angle 
180=angle+supplementary angle 
vertical angle 
cross line 
big/small angle 
parallel line 
Being Aggressive on Geometry Problems: whenever you have
a diagram, ask yourself What else do I know? write it down anyway.
ETS is also fond of disguising familiar figures within more complex
shapes by extending lines, overlapping figures, or combining several
basic shapes. So be on the lookout for the basic figures hidden in
complicated shapes.
Triangles
QUANDRILATERAL 
parallelogram 
quadrilateral in which opposite sides are parallel 
rectangule 
a parallelogram in which all angles equal 90º 
square 
rectangle in which all angles and all sides are equal 
TRIANGLES 
180 rules 
A=bh/2 
isosceles triangles 
s1=s2 
equilateral 
60 
pythagorean therorem 
a2+b2=c2 

3;4;5, 5:12:13 rues 
special right trangles 
306090: xsqrt(3)x2x (hypotenuse) 

454590:xxsqrt(2)x 
SOHCAHTOA 
opposite, adjacent,hypotenuse 

SOH:sine=opposite/hypotenuse 

CAH:cos=Adjacent/hypotenuse 

TOA:tangent=opposite/Adjacent 
similar triangles 
same shape(angles) 

diff size, same corresponding side ratio 
Circles
Circle 
radius 

diameter 

chord: any line segment in side circle 

arc:part of circumference(edge) 

circumference=2pi *radius 

area=pirr 
Proportionality 
Arc measure is proportional to interior angle measure, which is proportional to sector area. 

An interior angle is an angle formed by two radii. 

A sector is the portion of the circle between the two radii. 
tangents 
OPN=90;oQN=90; PNQ=45, 
Equation 
(x,y) is point of circle,(h,k) is the center, r is radius 

xy plane: (xh)^{2} + (yk)^{2}=r^{2} 
What is the center of a circle with equation x2 + y2 – 2x + 8y + 8 = 0 ?
Volume
ref to equation of volumes 
Plug in on Genometry
(Hidden )variable in choice answer 
180 rule for triangle 
outside angle=inner angle1+ingger angle2 
A rectangular box is half as long as it is wide and onethird as wide as it is
tall. If the volume of the box is 96, then what is its surface area?
imaginary and complex
sqrt(1) 
italicized i 
i^{n} 
i^{1}=i; i^{2}+1; i^{3}=i; i^{4}=1 

i^{5}=i; i^{6}+1; i^{7}=i; i^{8}=1 
complex number 
a+bi 

treat i as variable when do arithmetic 

add/subtraction ( distribute the minus sign) 

multiplication: FOIL 
Summary
Be sure to review your basic geometry rules before the test; often, problems hinge on knowing that vertical angles are equal or that the sum of the angles in a quadrilateral is 360°. 
On all geometry problems, draw figures out and aggressively fill in everything you know. 
When two parallel lines are cut by a third line, the small angles are equal, the big angles are equal, and the sum of a big angle and a small angle is 180°. 
The perimeter of a rectangle is the sum of the lengths of its sides. The area of a rectangle is length × width. 
The perimeter of a triangle is the sum of the lengths of its sides. The area of a triangle is 1/2 base × height. 
Knowing the Pythagorean Theorem, common right triangles (such as 345 and 5 1213), and special right triangles (45°45°90° and 30°60°90°) will help you figure out angles and lengths in a right triangle. 
For trigonometry questions, remember SOHCAHTOA: sine=opposite/hypotenuse; cosin=adjacent/hypotenus; tangent=opposite/adjacent 
Similar triangles have the same angles and their lengths are proportional. 
The circumference of a circle is 2πr. The area of a circle is πr2. 
Circles that show an interior angle (an angle that extends from the center of the circle) have proportionality. The interior angle over the whole degree measure (360°) equals the same fraction as the arc enclosed by that angle over the circumference. Likewise, both of these fractions are equal to the area of the segment over the entire area of the circle. 
When you see a line that is “tangent to” a circle, remember two things: The line touches the circle at exactly one point. The radius of the circle that intersects the tangent line is perpendicular (90°) to that tangent line. 
The formulas to compute the volumes of many threedimensional figures are supplied in the instructions at the front of both Math sections. 
When plugging in on geometry problems, remember to use your knowledge of basic geometry rules; e.g., there are still 180° in a triangle when you’re using Plugging In. 
The imaginary number i = , and there is a repeating pattern when you raise i to a power: i, –1, –i, 1. When doing algebra with i, treat it as a variable, unless you are able to substitute –1 for i2 when appropriate. 




