Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
72 Cards in this Set
 Front
 Back
What is a polygon?

Closed shape formed by line segments.


What is a quadrilateral?

Any four sided polygon.


What is a parallelogram?

Opposite sides are equal


What is rectangle?

All sides are 90 degrees, and opposite sides are equal.


What is a rhombus?

All sides are equal. Opposite angles are equal.


What is a square?

All angles are 90 degrees. All sides are equal.


What is a trapezoid?

One pair of opposite sides is parallel. In this case, the top and bottom sides are parallel, but the right and left sides are not.


The sum of the interior angles of a triangle is ______

180 degrees


The sum of the interior angles of a quadrilateral is ______

360 degrees


The sum of the interior angles of a pentagon is ______

540 degrees


The sum of the interior angles of a hexagon is ______

720 degrees


The sum of the interior angles of a polygon follows what pattern:

The sum of the angles is always 2 less than the number of sides * 180 degrees


Area of a triangle =

1/2 (base * height)


Area of a rectangle =

Length * Width


Area of a trapezoid =

((Base1 + Base2) * Height) / 2


Area of any parallelogram =

Base * Height


Area of a rhombus =

(Diagonal1 * Diagonal2) / 2


Surface area =

the SUM of the areas of ALL the faces


Volume or a rectangular solid / cube =

Length * Width * Height


What is the most important GMAT Geometry tool?

Cutting more complex polygons into RIGHT TRIANGLES


The sum of any two sides of a triangle must be ________

GREATER than the 3rd side


Equation for Pythagorean Theorem: What triangles does it apply to?

Right Triangles. A^2 + B^2 = C^2


Common right triangles:

345; 51213; 81517.


Key multiples of common right triangles

6810; 91215; 121620; 102426


Isosceles triangle are one in which ________

Two sides and their corresponding angles are equal.


The most important isosceles triangle on the GMAT is the:

Isosceles right triangle. 454590 triangle.


What is the ratio of the legs of a 454590?

a:a:a√2


A square divides into what?

Two 454590 triangles.


What is an equilateral triangle? What does it divide into?

All angles and sides are equal. It divides into a 306090 triangle.


What is the ratio of the legs of a 306090 triangle?

a:a√3:2 [306090]


The side of an equilateral triangle is the same as the ______ of a 306090 triangle.

SIDE of equilateral = HYPOTENUSE of 306090 triangle


The height of an equilateral triangle is the same as the ______ of a 306090 triangle.

HEIGHT of equilateral = LONG LEG of the of 306090 triangle


Diagonal of a square =

d = s√2, where s is a side of the square


The diagonal of a cube can be found using the formula

d = s√3, where s is an edge of the cube


To find the diagonal of a rectangle, you must know ___ or ____

Length and Widge OR one dimension and the proportion of one to the other.


If rectangle has width of 6 and a ratio of the Width to Length is 3:4, what is the diagonal?

8


What is the length of the diagonal of a rectangular solid? 8x9x12

Use pythagorean theorem twice: Diagonal of bottom face: 9^2 + 12^2 = c^2 yields c = 15. Then 15^2 + 8^2 = c^2. c = 17.


Triangles are defined as similar if:

all their corresponding angles are equal and their corresponding sides are in proportion.


How do you tell if two triangles are similar?

If two angles are the same, (congruent), then the two triangles are similar.


If you know the ____, ___, ____, ___, you can use one to find any of the other measurements.

Circumference, radius, diameter, or area of a circle, you can use one to find any of the other measurements.


Any line segment that connects two points on a circle is called a _____

chord


Circumference of circle:

C = 2Πr


Arc length can be found by:

Determining what fraction the arc is of the entire circumference. This can be done by looking at the central angle that defines the arc.


Area of a circle

A = Πr^2


Area of a sector of a circle

Find out what fraction the sector is of the entire circle.


What is a central angle?

An angle whose vertex lies at the center point of the circle.


What is an inscribed angle?

An inscribed angle has its vertex on the circle itself.


Which angle defines the arc of a circle?

Central angle


An inscribed angle is equal to ____ of the arc it intercepts

1/2 of the arc it intercepts.


If you are given the measure of an inscribed angle, find the measure of the _______ to solve the problem

Find the measure of the corresponding central angle to solve the problem.


If a triangle is inscribed in a circle, such that one of its sides is a diameter of the circle, then

the triangle MUST be a right triangle.


Any right triangle inscribed in a circle, must have one of its sides as a ______

diameter of the circle (thereby splitting the circle in half).


A cylinder is made up of what two shapes:

two circles and a rectangle.


To determine the surface area of a cylinder:

2(Πr^2) + 2Πrh


Volume of a cylinder:

V = Πr^2*h


Slope of a line

rise / run (change in y / change in x)


Four types of slope

positive, negative, zero slope (horizontal line), undefined slope (vertical line)


Describe Y intercept

Where the line hits the yaxis (where x = 0) or (0,y)


Describe Xintercept

Where the line hits the xaxis (where y = 0) or (x,0)


All lines can be written as equations in the form

y = mx + b m = slope, b = yintercept


Horizontal lines are expressed as:

y = some number


Vertical lines are expressed as:

x = some number


Given any two points on a line, you should be able to write an equation in y = mx + b format…How?

Find slope. Plug in slope for m in slope intercept equation and solve for b, by plugging in a point. Write equation.


What is the distance between any two points in the coordinate plane?

Draw a right triangle connecting the two points. Find the two legs by calculating rise and run. Use pythagorean theorem to find distance between two points.


Quadrant I:

positive xcoordinate, positive ycoordinate


Quadrant II:

negative xcoordinate, positive ycoordinate


Quadrant III:

negative xcoordinate, negative ycoordinate


Quadrant IV:

positive xcoordinate, negative ycoordinate


What is the perpendicular bisector of a line segment?

Line forming 90degree angle with segment and divides segment exactly in half.


Perpendicular lines have ________ slopes

negative inverse slopes.


A central angle that describes an arc that is proportional to a fractional part of _____

360 degrees


An inscribed angle describes an arc that is proportional to a fractional part of_____

180 degrees
