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Standardized Tests Math and Science Practice

Geometry Review

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Angles Review

Angle CMB = Angle AMD
Angle AMD + Angle CMA = 180^o

Example of SAT question with angles:In the figure below, angle AMB is 100^o, angle BMD is 40^o and angle CME is 60^o. What is the value of angle CMD?
Figure not drawn to scale

(a) 20^o
(b) 30^o
(c) 40^o
(d) 50^o
(e) 80^o

Answer: If angle AMB is 100^o, then angle BME is 180^o - 100^o = 80^o
BMC + CMD = 40^o
BMC + CMD + DME = 80^o
If we subtract the 2 equations, DME = 40^o
CMD + DME = 60^o
BMC + CMD + DME = 80^o
If we subtract the 2 equations, BMC = 20^o
CMD = BME - BMC - DME = 80^o - 40^o - 20^o = 20^o

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 = 180^o

The sum of the measures of the interior angles of a polygon is:
(n - 2)·180^o
n = number of sides of the polygon.

The sum of the measures of the interior angles of the polygon above is (5 - 2)·180^o = 540^o

AC² = AB² + BC².

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

Equilateral triangle.
a = b = c = 60^o
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

Exemple of SAT Subject geometry problem