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Manhattan GMAT Prep Geometry
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Terms in this set (31)
Universal Sum of Interior angles Equation
(n-2)180
Are the Units of a Polygon's Area squared?
yes
Area of a triangle
1/2(B*H)
Area of a rectangle
L*W
Area of a trapezoid
1/2(Base1 + Base2) * Height
will have to draw height in
Area of Parallelogram
Base x Height
will have to draw height in
Rhombus
1/2(Diagonal1 * Diagonal2)
Surface area of Rectangular Solid
2(wl + hl+hw)
Surface area of Cube
the sum of all the faces: 6(s^2)
Volume
length x width x height. The Units are cubed
What must you I know to answer a question about fitting 3D objects into other 3D objects?
The specific volume, because the respective volume is not sufficient.
Characteristics of a Right Triangle
1 90 degree angle
Two Legs, 1 hypotenuse
In a right triangle, what is unique about side C?
It is usually the hypotenuse and opposite the right angle.
Given 2 side of a right triangle, what can be used to find the third side?
Pythagorean Theorem
a^2 + b^2 = c^2
What are the most common right triangles used on the GMAT?
3-4-5
5-12-13
8-15-17 (least popular)
What are common multiples for the 3-4-5 triangle ?
6-8-10
9-12-15
12-16-20
What are common multiples for the 5-12-13 triangle ?
10-23-26
Characteristics of a Isosceles Triangle
2 equal sides, 2 equal angles
Isosceles Right Triangle
45-45-90
Exactly half of a square. Hence if given the diagonal of a square, you can find it's sides.
Ratios for leg length of Isosceles Right Triangle
45 45 90
leg leg hypotenuse
1 : 1 : √2
x : x : x√2
Characteristics of an Equilateral Triangles
All sides equal, all angles = 60 degrees
30-60-90 Triangle
Relative of the equilateral triangle: half of the equilateral
Ratios for 30-60-90 triangle
can be used to find measurements of the equilateral triangle
30 60 90
short long hypotenuse
1 : √ 3 : 2
x : x√3 : 2x
Similar Angles
all angles equal, Corresponding Sides are proportional
If ratio of similar triangles is a:b, that is ratio of its angles?
a^2:b^2
Any similar polygon, what is the ratio of side length to area?
if a:b, then a^2: b^2
What can one use to find the diagonal of other polygons?
right triangles
Diagonal of a Square
d= s√2 , s= side of a square
this is also the face diagonal of a cube
Main diagonla of a cube
d = s√3 , s= edge of a cube
Diagonal of a Rectangle
must know the length and width or
one of the two dimensions and the ratio of one to the other
use a^2+b^2=c^2
Diagonal of a Rectangular Solid
d^2= x^2+ y^2+z^2
x, y, z= sides of a rectangular solid
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