# GMAT Geometry

## 33 terms

### Parallelogram

opposite sides and opposite angles are equal

### rhombus

all sides are equal, opposite angles are equal

### trapezoid

one pair of opposite sides is parallel

(n-2) * 180

### Area of a Triangle

(Base * Height)/2

### area of a Trapezoid

((Base 1 + Base 2)* Height ) /2

the height refers to a line perpendicular to the 2 bases, which are parallel.
-can also be cut into 2 right triangles and 1 rectangle

### Area of any Parallelogram

Base * Height

the height is the line perpendicular to the base, like the trapezoid, you often have to draw in the height.

### Area of a Rhombus

(Diagonal 1 * Diagonal 2) /2

the diagonals of a rhombus are Always perpendicular bisectors.

### volume of rectangular solid

length width height

180

### angles correspond to their opposite sides

-this means that the largest angle is opposite the longest, while the smallest angle is opposite the smallest.
-if two sides are equal, their opposite angles are also equal

### The Sum of any two sides of a Triangle

must be GREATER than the third side

### sum of two sides of a triangle

the length of the 3rd side must lie between the difference and the sum of the two given sides

key multiples:
6-8-10
9-12-15
12-16-20

10-24-26

### Isosceles Triangle and the 45-45-90 Triangle

a triangle where two sides and opposite angles are equal.
x - x - x sqrt2

(this triangle is exactly half of a square)

### Equilateral Triangle and the 30-60-90 Triangle

two 30-60-90 triangles form an equilateral triangle.

short leg - long leg - hypotenuse
x - x sqrt3 - 2x

### diagonal of a square

d = s(sqrt2), where s is a side of the square

### diagonal of a cube

d = s(sqrt3), where s is an edge of the cube

### similar triangles

corresponding angles are equal and corresponding sides are in proportion

### area of similar triangles

if two similar triangles have corresponding side lengths in ratio a:b, then their areas will be in ratio a^2 : b^2

C = 2pier

A = pie * r^2

### Inscribed vs. Central Angles

An inscribed angle is equal to half of the arc that it intercepts, in degrees.

### Inscribed Triangles

if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle must be a right triangle

### Cylinder Surface Area

SA = 2 circles + rectangle = 2(pier^2) + 2pie*rh

V = pier^2h

### Exterior Angles of a Triangle

An exterior angle of a triangle is equal in measure to the sum of the two non-adjacent (opposite) interior angles of the triangle.

### the Distance between 2 Points

d = sqrt( ( x2 - x1)^2 + (y2 - y1)^2)

or alternatively, you can draw a triangle by connecting the two points and solve for the hypotenuse.

### Perpendicular Bisectors

the perpendicular bisector has the negative reciprocal slope of the line segment it bisects. That is, the product of the two slopes is -1

### Parallel lines

parallel lines have equal slopes

### perpendicular lines

have negative reciprocal slopes

### the Intersection of Two Lines

two lines that intersect share a point that solves both equations.
If two lines in a plane do not intersect, then the lines are parallel.