SAT考試幾何部分常用公式
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
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
