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GMAT Math > Geometry > Flashcards

Geometry Flashcards

1
Q

Three Rules to Live by in Geometry

A

1) If they don’t tell you, don’t assume.
2) If they give you something, use it.
3) Know rules and formulas

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2
Q

Inscribed means

A

lies inside and vertices touch the other shape; indicates relationships between them

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3
Q

Area of a square

A

s^2

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4
Q

Area of a rectangle

A

L x W

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5
Q

Area of a triangle

A

1/2bxh

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6
Q

What is height in a triangle

A

Perpendicular line from base to the top of the triangle in reference to that base (base can be any of the three sides)

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7
Q

Area of a trapezoid

A

((b1 + b2) / 2) x h

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8
Q

Area of a parallelogram

A

b x h (need to find height)

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9
Q

Perimeter of square

A

4 s

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10
Q

Perimter of rectangle

A

2L + 2W

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11
Q

Perimeter of a triangle

A

x + y + z (all sides added up)

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12
Q

Perimeter of a parallelogram

A

2L + 2W

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13
Q

Area of a circle

A

πr^2

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14
Q

Circumference of a circle

A

2πr or πd

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15
Q

Area of a sector

A

find Area of sector as a percentage of area of circle (ratio of angles will tell you this), then solve after know something about area of circle

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16
Q

Arc length

A

Length of circumference; must find circumference and then relate amount of arc as sector of circle (using angles) and determine what portion it represents

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17
Q

Central angle

A

Vertex of a central angle is the center

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18
Q

Inscribed Angle

A

One shape within another, where vertices touch on edge of shape

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19
Q

If Inscribed triangle has hypotenuse as diameter…

A

is a right triangle

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20
Q

Relationship of central angle to inscribed angle (sectors)

A

central angle is 2x relative to the inscribed angle with the same end points.

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21
Q

Special Right Triangles

A

45-45-90

30-60-90

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22
Q

45-45-90 Triangle side length relationships

A

x (leg), x (leg), x√2 (hypotenuse)

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23
Q

30-60-90 Triangle side length relationships

A

x (shorter leg), x√3 (longer leg), 2x (hypotenuse)

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24
Q

Equilateral Triangle

A

All sides of equal length, angels are 60 each

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25
Q

Isosceles Triangle

A

Two sides and two angles are even

26
Q

Pythagorean Triples

A

3-4-5
6-8-10 (or other multiples of 3-4-5)
5-12-13 (or 10-24-26)
8-15-17

27
Q

Similar Triangles

A

Triangles with same angles have proportionate sides

28
Q

Relationship of angles and sides

A

Angle size corresponds to side length size (referring to the side length opposite the angle

29
Q

Volume of a 3D rectangular shape

A

l x w x h

30
Q

Surface area of a 3D rectangular shape

A

2 x (LxW + LxH + WxH)

31
Q

Volume of a cube

A

s^3

32
Q

Surface Area of a cube

A

6s^2

33
Q

Volume of a cylinder

A

πr^2h

34
Q

Surface Area of a cylinder

A

2(πr^2) + 2πrh

35
Q

Slope

A

Rise over Run

y1 - y2 over x1-x2

36
Q

Intersecting Lines Rules

A

Interior angles add to 360°
Interior angles that combine to form a line sum to 180°
Angles found opposite each other where two lines intersect are equal (vertical angles)

37
Q

Parallel Lines cut by a transveral rules

A

Watch for this to be disguised (remember the Z)
Eight angles are formed, but there are only 2 distinct angles; draw and label them a° and b°; a + b = 180
A is the acute less than 90°; B is the obtuse greater than 90°

38
Q

Polygon Sum of Interior Angles

A

(n-2) x 180°

39
Q

Length range of third side of a triangle

A

sides are a b c

b-a

40
Q

Exterior Angles of a Triangle

A

Exterior angle is equal to the sum of the two non-adjacent interior angles of the triangle

41
Q

Circle Radius, Diamter, Circumference and Area

A

Know one value, can figure the rest

42
Q

Describe 4 quadrants, counterclockwise (coordinate plane)

A 
Quad 1 upper right hand corner (positive y, positive x)
Quad 2 (Positive y, negative x)
Quad 3 (negative y, negative x)
Quad 4 (negative y, positive x)
43
Q

Vertical line slope

Horizontal line slope

A

x = 0 (or some other number) (undefined) (vertical line)

y = 0 (or some other number) slope is 0 (horizontal line)

44
Q

Area of rhombus

A

(Diagnol 1 x Diagnol 2)/2

45
Q

Max area of a quadrilateral

A

closest to square

46
Q

Minimum perimeter

A

square

47
Q

Sector calculations

A

Central angle / 360, sector area / circle area, and arc length / circumference

48
Q

Parallelogram diagnols

A

Make equal triangles, cut angles in half, bisect each other

49
Q

Geometry process

A

1) draw or redraw figures, fill in all given info, identify target
2) identify relationships and create equations
3) solve equations for missing value
4) Make inferences from figures

50
Q

Perimeter of a sector

A

2r + arc length

51
Q

Similar shapes have sides in ratio a:b, have areas in ratio…

A

a^2 : b^2

52
Q

Maximize area of a polygon for given perimeter

A

Make side lengths as close to equal as possible

53
Q

Minimize perimeter for given area of a polygon

A

Make sides as close to equal as possible

54
Q

Maximize area of a triangle or parallelogram

A

Put known sides perpendicular to each other

55
Q

A of an equilateral triangle

A

(s^2sqrt3)/4

56
Q

Diagnol of cube

A

s* sqrt 3

57
Q

Slope of perpendicular bisectors

A

Negative reciprocal

58
Q

Point of intersection of bisector

A

X = average of x coordinates

Y = average of y coordinates

59
Q

Point of intersection of two lines

A

Point solves two equations - solve as a system of equations

If parallel lines, never intersect

If same line in different forms, will intersect infinitely at every point

60
Q

Characteristics of quadratic function graphs

f(x)=ax^2 + bx + c

A

a>0, curve opens up

a

61
Q

How many times will a quadratic graph touch x axis? How solve for these?

A

Find by plugging points

Solve the quadratic - factoring

Use discriminat b^2 - 4ac, use quadratic formula

GMAT Math (12 decks)

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