SAT考试几何部分常用公式

　　Angles Review

　　Angle CMB = Angle AMD

　　Angle AMD + Angle CMA = 180o

　　Example of SAT question with angles:In the figure below, angle AMB is 100o, angle BMD is 40o and angle CME is 60o. What is the value of angle CMD?

　　Figure not drawn to scale

　　 20o

　　 30o

　　 40o

　　 50o

　　 80o

　　Answer: If angle AMB is 100o, then angle BME is 180o - 100o = 80o

　　BMC + CMD = 40o

　　BMC + CMD + DME = 80o

　　If we subtract the 2 equations, DME = 40o

　　CMD + DME = 60o

　　BMC + CMD + DME = 80o

　　If we subtract the 2 equations, BMC = 20o

　　CMD = BME - BMC - DME = 80o - 40o - 20o = 20o

　　Parallel Lines Review

　　If the 2 horizontal lines are parallel,

　　- angles 1 = 3 = 5 = 7 and

　　- angles 2 = 4 = 6 = 8

　　Polygons Review

　　The sum of the measures of the interior angles of a triangle is 180.

　　a + b + c = 180o

　　The sum of the measures of the interior angles of a polygon is:

　　180o

　　n = number of sides of the polygon.

　　The sum of the measures of the interior angles of the polygon above is 180o = 540o

　　AC2 = AB2 + BC2.

　　Pythagorean Theorem applied to the triangle above: AC2 = AB2 + BC2.

　　Equilateral triangle.

　　a = b = c = 60o

　　AB = BC = CA

　　Isosceles triangle.

　　b = c

　　AB = AC

　　a b.

　　BC AC

　　In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

　　Area, Perimeter and Volume

　　Rectangle Perimeter

　　2a + 2b

　　Rectangle Area

　　ab

　　Triangle Perimeter

　　AB + BC + CA

　　Triangle Area

　　BC

　　Circle Perimeter

　　2Circle Area

　　Cube Volume

　　a3

　　Cylinder Volume