SAT数学考试几何部分常用公式

2022-06-04 10:56:41

  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

  (a) 20o

  (b) 30o

  (c) 40o

  (d) 50o

  (e) 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:

  (n - 2)·180o

  n = number of sides of the polygon.

  The sum of the measures of the interior angles of the polygon above is (5 - 2)·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> c > b.

  BC > AB > 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

  2·a + 2·b

  Rectangle Area

  a·b

  Triangle Perimeter

  AB + BC + CA

  Triangle Area

  (h/2)·BC

  Circle Perimeter

  2·Circle Area

  Cube Volume

  a3

  Cylinder Volume

热门院校