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Standardized Tests Math and Science Practice






Geometry Review

SAT Geometry

Dr. John Chung’s SAT Math

 

 


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·¶·r Circle Area ¶·r2



Cube Volume a3






Cylinder Volume h·¶·r2





Examples of SAT Geometry Questions GED Practice Exemple of SAT Subject geometry problem