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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:
3-4-5; 5-12-13; 8-15-17.
Key multiples of common right triangles
6-8-10; 9-12-15; 12-16-20; 10-24-26
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. 45-45-90 triangle.
What is the ratio of the legs of a 45-45-90?
A square divides into what?
Two 45-45-90 triangles.
What is an equilateral triangle? What does it divide into?
All angles and sides are equal. It divides into a 30-60-90 triangle.
What is the ratio of the legs of a 30-60-90 triangle?
a:a√3:2 [30-60-90]
The side of an equilateral triangle is the same as the ______ of a 30-60-90 triangle.
SIDE of equilateral = HYPOTENUSE of 30-60-90 triangle
The height of an equilateral triangle is the same as the ______ of a 30-60-90 triangle.
HEIGHT of equilateral = LONG LEG of the of 30-60-90 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?
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 _____
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 y-axis (where x = 0) or (0,y)
Describe X-intercept
Where the line hits the x-axis (where y = 0) or (x,0)
All lines can be written as equations in the form
y = mx + b m = slope, b = y-intercept
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 x-coordinate, positive y-coordinate
Quadrant II:
negative x-coordinate, positive y-coordinate
Quadrant III:
negative x-coordinate, negative y-coordinate
Quadrant IV:
positive x-coordinate, negative y-coordinate
What is the perpendicular bisector of a line segment?
Line forming 90-degree 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