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GMAT > Geometry > Flashcards

Geometry Flashcards

1
Q

What are supplementary angles?

A

Sum of angles equal 180deg

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2
Q

What are complementary angles?

A

Sum of angles equal 90deg

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3
Q

A cyclic quadrilateral (quad with vertices on circle circumference) have what property?

A

Opposite angles are supplementary (sum equals 180deg)

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4
Q

For a regular polygon, what are the equations to find the:
1. Interior Angles
2. Exterior Angles

A
  1. IA = (n-2)/2 x 180deg
  2. EA = 360/n
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5
Q

For any polygon, what are the equations to find the sum of the:
1. Interior Angles
2. Exterior Angles

A
  1. Sum(IA) = (n-2) x 180deg
  2. Sum(EA) = 360
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6
Q

What are the two equation forms of a linear line in coordinate geometry?

A
  • Standard: ax + by +c = 0
  • Slope/Intercept: y = mx +c
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7
Q

In coordinate geometry, when a linear equation has 1 variable, it has what relationship to the axes?

A

It is parallel to one of the axes

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8
Q

How do you calculate the midpoint between 2 coordinates?

A

MP = ( (X1+ X1)/2, (Y1 + Y1)/2)

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9
Q

How do you find the gradient between 2 points?

A

(y2 - y1) / (x2 - x1)

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10
Q

How do you calculate the distance of coordinates from the origin?

A

Distance = sqrt((x^2) + (y^2))

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11
Q

In coordinate geometry, how do you calculate the distance between two points?

A

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

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12
Q

If a triangle on a coordinate plane has no sides parallel to the axis, how do you find the area?

A

Area under the graph - Area not included

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13
Q

In a coordinate plane how do you know if 2 lines are perpendicular?

A

Product of gradients =1
IOW gradients are reciprocal
OR
(a1a2) = (b1b2)

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14
Q

What is the area of a trapezium?

A

A = (1/2)(a+b)h

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15
Q

In a coordinate plane how do you know if 2 lines intersect?

A

(a1/a2) =/= (b1/b2)

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16
Q

In a coordinate plane how do you know if 2 lines are coincident?

A

(a1/a2) = (b1/b2) = (c1/c2)

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17
Q

In a coordinate plane how do you know if 2 lines are parallel?

A

(a1/a2) = (b1/b2) =/= (c1/c2)

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18
Q

For a cuboid how do you find:
1. Body Diagonal
2. Face Diagonal
3. Minimum surface distance?

A
  1. db = sqrt(l^2 + w^2 + h^2)
  2. df = sqrt(l^2 + w^2)
  3. Min SD = sqrt(l^2 + (w + h)^2)
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19
Q

When two tangents on a circle meet at a point, what is the relationship between the tangents?

A

They are equal length

20
Q

How do you find the diameter for:
1. A cylinder in a cube
2. A cube in a cylinder

A
  1. d = side
  2. d = df = sqrt(2) . side
21
Q

How do you find the area of a segment?

A

(pi) . r^2 . (angle/360) - area of triangle

Angle/360 is equal to the number of sectors if the sectors are equal

22
Q

How do you find the length of:
1. Minor arc
2. Major arc

A
  1. Minor arc = (2x pi x r x angle)/360
  2. Major arc = (2x pi x r x (360-angle))/360
23
Q

All angles in a segment =?

24
Q

How do you find the area of a sector?

A

(pi) . r^2 . (angle/360)

Angle/360 is equal to the number of sectors if the sectors are equal

25
Q

How do you find the diameter for:
1. A sphere in a cube
2. A cube in a sphere

A
  1. d = cube side length
  2. d = cube body diagonal = s x sqrt(3)
26
Q

If an equilateral triangle is inscribed in a circle, r = ?

A

r = side/(sqrt(3))

27
Q

If a circle is inscribed in an equilateral triangle, r = ?

A

r = side/(2.(sqrt(3)))

28
Q

For a cube how do you find:
1. Body Diagonal
2. Face Diagonal
3. Minimum surface distance?

A
  1. db = sqrt(3) . side
  2. df = sqrt(2) . side
  3. Min SD = sqrt(5) . side
29
Q

For a hemisphere how do you find:
1. Curved Surface Area
2. Total Surface Area
3. Volume?

A
  1. Curved SA = 2(pi)(r^2)
  2. Total SA = 3(pi)(r^2)
  3. Volume = (2/3)(pi)(r^3)
30
Q

For a sphere how do you find:
1. Total Surface Area
2. Volume?

A
  1. SA = 4(pi)(r^2)
  2. Volume = (4/3)(pi)(r^3)
31
Q

What is the area of a trapezium?

A

A = (1/2)(a+b)h

32
Q

For a regular polygon, the perimeter is what when the area is what?

A

Perimeter is maximum when area is minimum
Perimeter is minimum when area is maximum

33
Q

How do you find the central angle of a regular polygon?

A

360deg/n

n is the number of sides

34
Q

What is the equation for the diagonal of a square?

35
Q

The diagonals of a rhombus have what relationship?

A

They are perpendicular

36
Q

What is the equation for the diagonal of a rectangle?

A

Diagonal = sqrt((b^2) + (h^2))

37
Q

What are the 3 methods to find if two triangles are congruent?

A
  1. SAS
  2. SSS
  3. SAA
38
Q

The diagonals of a rectangle have what relationship?

A

The bisect eachother and so, have equal length

39
Q

What is the relationship between z^2 and (x^2 + y^2) for:
1. * An acute triangle
1. * An obtuse triangle ?

A
  1. z^2 < x^2 + y^2
  2. z^2 > x^2 + y^2
40
Q

Congruent triangles have what relationship?

A
  1. All respective sides are the same
  2. All respective angles are the same
41
Q

Similar triangles have what relationship?

A
  1. All respective sides are proportional
  2. All respective angles are the same
42
Q

When diagonals bisect you make 2 (what) triangles?

43
Q

What are the 3 methods to find if two triangles are similar?

A
  1. SAS
  2. SSS
  3. AA
44
Q

For a triangle with sides A, B, C what is the relationship with C if:
1. * A + B
2. * A - B?

A
  1. A + B > C
  2. A - B < C
45
Q

How do you solve: What is the difference between the area/volume of a shape and the shape with a maximum error (x)

A

Add the error to the original dimensions to find the individual difference for l, w, h and sum the differences

sum(diff) = l(diff) + w(diff) + h(diff)

GMAT (14 decks)

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