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GMAT > Geometry > Flashcards

Geometry Flashcards

0
Q

What do the exterior angles of a triangle add to?

A

360

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1
Q

What do the interior angles of a triangle add to?

A

180 Degrees

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2
Q

What is the area of a triangle formula?

A

Area = (1/2)(B)(H)

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3
Q

What is the Pythagorean theorem?

A

A^2 + B^2 = C^2

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4
Q

What is an equilateral triangle?

A

All sides are equal. All angles = 60 degrees. When an equilateral triangle has an angel bisected it becomes a 30/60/90 triangle.

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5
Q

What is an isosceles triangle?

A

Two sides are equal and two angles are equal

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6
Q

What is area of a circle?

A

Area = (pie)(r^2)

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7
Q

What is the circumference of a circle?

A

Circumference = (pie)(D) = 2(pie)(r)

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8
Q

What do you need to find the arc-length or arc degree of a circle?

A

The degree of an arc/360 is proportional to the area and circumference of a circle

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9
Q

What is the relationship between a radius and a diameter?

A

(2)(radius) = diameter

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10
Q

What are the total degrees in a circle?

A

360

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11
Q

What is the volume of a rectangular solid?

A

Base times height

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12
Q

What do two angles on a line equal?

A

180 degrees

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13
Q

What do angles around an intersection of at least two lines add to?

A

360 Degrees

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14
Q

Do parallel lines ever cross?

A

Not on a 2D plane. Not if they are on the same plane.

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15
Q

If a triangle is inscribed inside a circle so that one side of the triangle is a diameter. What type of triangle is it?

A

A right triangle.

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16
Q

If given a radius of a circle what can you determine?

A

Circumference, diameter, area. All other necessary values on the GMAT

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17
Q

What is a tangent line?

A

A line that touches a circle on exactly one point. It’s perpendicular to the radius at the point if tangency.

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18
Q

What axis is vertical?

A

Y axis

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19
Q

What axis is horizontal

A

X axis

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20
Q

What is the slope formula?

A

Rise/Run - (Y1 - Y2)/(x2 - x1) - (Delta Y / Delta X)

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21
Q

How are points written?

A

(X, Y)

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22
Q

What is the line formula?

A

Y = mx + b

M is slope
B is y intercept
(X,y) is a point on the line

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23
Q

What is the theory of triangle sides?

A

Two sides added together are always longer than the third side. The difference of any two sides is less than the third side.

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24
Q

Area if a rhombus?

A

A = (b)(h)

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25
Q

Area of a trapezoid?

A

A = (1/2)(b1 + b2)(h)

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26
Q

What is pie?

A

Circumference/Diameter. Infinite # 22/7 is close. 3.14 is also close.

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27
Q

What is 0/x =

A

Zero slope/Horizontal line

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28
Q

What is a 0 slope look like?

A

A horizontal Line

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29
Q

What does an undefined slope look like?

A

Vertical line. X/0

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30
Q

What is the slope of a vertical line?

A

Undefined/No Slope - Cannot divide anything by 0. (X/0 = Undefined)

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31
Q

Name two unique degree combinations in right triangles and the corresponding sides.

A

45: 45:90 X:X:Xsq.2
30: 60:90. X:Xsq3:2X

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32
Q

What are the two common Pythagorean triples?

A

3: 4:5
5: 12:13

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33
Q

x:12:13

A

5:12:13

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34
Q

5:x:13

A

5:12:13

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35
Q

5:12:x

A

5:12:13

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36
Q

What happens when you draw a diagonal in a parallelogram?

A

You bisect the area and if you have two lines they bisect each other

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37
Q

Def: Paraelleogram

A

Closed quadrilateral with two sets of parallel lines. Rectangles, squares, rhombus.

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38
Q

Volume of a rectangular solid?

A

V = (l)(w)(h)

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39
Q

Surface area of a rectangular solid?

A

SA = 2( lw + lh + wh) (the faces)

40
Q

Volume of a cylinder?

A

Base x height. = (pie)(r^2)(h)

41
Q

Surface area if a cylinder?

A 
SA = (faces)(lateral surface area)
SA = ((2)(pie)(r^2)) + ((2)(pie)(r)(H))
42
Q

What is the lateral surface area?

A

Surface area of the cylinder height only. Does not include the faces. LSA=(circumference)(height)

43
Q

Area of a Parallelogram?

A

Area = (b)(h)

44
Q

Interior angles of a parallelogram add to?

A

360 degrees

45
Q

How many sides does a polygon with 360 degree angles have?

A

4 sides

46
Q

Area of a trapezoid?

A

Area=(1/2)(b1 +b2)(h)

47
Q

How many sides are parallel in a trapezoid?

A

At least one set. If it’s two sets of parallel lines it’s a parallelogram.

48
Q

Are all trapezoids parallelograms?

A

No

49
Q

Are all parallelograms trapezoids?

A

Yes

50
Q

Describe the height of a triangle

A

Distance from base to opposing apex. Must be perpendicular to base. Any side can be a base.

51
Q

A 45:45:90 triangle is 1/2 a what?

A

Square

52
Q

When an altitude is drawn from the unequal side of an isosceles triangle is does what?

A

Bisects the base and the angle.

53
Q

What does congruent mean?

A

Equal

54
Q

Every equilateral triangle is also what type of triangle?

A

An Isosceles triangle. All isosceles triangles are not equilateral triangles.

55
Q

What does the height of an equilateral triangle always equal?

A

(Sq root 3)(x)/(2)where x is the side of the triangle.

56
Q

What is a chord?

A

A line connecting two points in a circle that doesn’t necessarily go through the center of the circle.

57
Q

Describe a diameter in terms of a chord.

A

A chord that goes through the center of a circle.

58
Q

What is a central angle?

A

An angle that starts in the center if a circle.

59
Q

What is an inscribed angle in a circle?

A

It’s inside the circle and it starts from the circumference as opposed to a central angle that starts in the center of a circle.

60
Q

If multiple inscribed angles in a circle share the same arc describe the angles.

A

They are all equal to one another if they share the same arc and they are all inscribed.

61
Q

Describe the relationship of a central angle and an inscribed angle share the same arc.

A

The central angle is twice the inscribed angle. The inscribed angle is half the central angle.

62
Q

What can you find if you have an inscribed angle and a radius?

A

All of it! Area/circumference/length arc.

63
Q

What’s the slope of parallel lines?

A

The same.

64
Q

What’s the slope of a perpendicular line?

A

The negative reciprocal of the other line.

65
Q

If you increase the slope what happens to the line ?

A

It gets steeper.

66
Q

What’s the direction of a positive slope?

A

Northeast

67
Q

What’s the direction if a negative slope?

A

Southeast

68
Q

Describe the quadrants in coordinate geometry.

A

Starts in the (pos,pos) quadrant with 1 and then moves counter clockwise.

69
Q

How do you find the x intercept?

A

Set y to zero or use the formula = (-b)/m

70
Q

Describe the slope of two lines if the product of them equals -1.

A

They are perpendicular.

71
Q

What is the distance between two points?

A

=sq root{(x1 - x2)^2 + (y1 - y2)^2}

72
Q

Midpoint formula?

A

={(x1 + x2)/2, (Y2 + y1)/2}

73
Q

How do you determine the number of degrees inside a polygon?

A

=(n-2)(180) where n=the number of sides

74
Q

What is a rhombus vs trapezoid?

A

Rhombus - Two sets of parallel lines without right angles. Trapezoid - One set of parallel lines in a quadrilateral. All parallelograms are trapezoids.

75
Q

Describe a major vs a minor arc.

A

The minor arc is the smaller arc. The major arc is the other/outer arc.

76
Q

What are uniform solids?

A

If you cut them into cross sections that would have the same bases as the original.

77
Q

What is a vertex? What is he plural version of this?

A

A corner in a polygon. Plural: Vertices

78
Q

What are supplementary angles?

A

The add to 180

79
Q

What are complementary angles?

A

Add to 90 degrees

80
Q

What are bisected angles?

A

An angle that is split evenly.

81
Q

What are adjacent angles?

A

The are next to each other on a straight line.

82
Q

Area of a parallelogram

A

Area = (base)(height)

83
Q

What are vertical angles ?

A

Just like it says. If two lines cross they are he angles across from each other.

84
Q

What is a transversal?

A

A line that crosses parallel lines.

85
Q

What is the origin?

A

Point (0,0) on coordinate geometry.

86
Q

What is the altitude?

A

The height

87
Q

Describe legs/base in a triangle.

A

There are two legs and 1 base.

88
Q

How many sides in a pentagon?

A

5

89
Q

How many sides in a hexagon?

A

6

90
Q

What is a semicircle?

A

Half a circle. A circle cut by its diameter

91
Q

What is the exterior angle of a triangle equal to?

A

The sum of the other two interior angles.

92
Q

What is a regular polygon?

A

A polygon with equi-angles and equi-sides.

93
Q

What is a polygon?

A

A closed plane figure formed by three or more line segments.

94
Q

What makes triangles congruent?

A

Equal angles and equal sides. Basically, equal triangles.

95
Q

Sometimes the height of a triangle is outside of the triangle.

A
96
Q

72 degrees

A

1/5 a circle

97
Q

1/6 a circle

A

60 degrees

GMAT (6 decks)

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