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Gmat > Geometry > Flashcards

Geometry Flashcards

1
Q

Angles that form a straight line measure…

A

180 degrees

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2
Q

A transversal forms how many angles ?

A

8

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3
Q

Describe a transversal

A

A line that intersects two or more parallel lines

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4
Q

What are the two distinct angles a transversal forms ?

A

A big angle larger than 90 degrees. And a small angle smaller than 90 degrees

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5
Q

What is the sum rule to remember for transversals ?

A

The sum of any big angle and small angle formed by a transversal is 180 degrees

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6
Q

What should you always do when working with a problem with a transversal?

A

Label all 8 angles so that angle relationships are easier to distinguish

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7
Q

What do you call a line that splits an angle or line segment in half

A

A bisector

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8
Q

What is a midpoint?

A

Any point that lies in the middle of a line segment

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9
Q

How do you approach a number line problem?

A

Label the line segments

Set up equations and Rewrite the given information algebraically

Plug the equation into one another

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10
Q

What is a polygon?

A

A closed figure formes by 3 or more line segments

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11
Q

What do you call the line segments of a polygon?

A

Sides

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12
Q

What is a point of intersection between two sides called

A

Vertex

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13
Q

What do you call the distance around a polygon

A

Perimeter

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14
Q

How do you calculate perimeter of a polygon?

A

Add the lengths of its sides

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15
Q

The area of a polygon is measured in terms of

A

Square units

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16
Q

What do you call angles located within a polygon?

A

Interior angles

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17
Q

Number of interiors angles is equivalent to …?

A

Number of sides

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18
Q

What is the formula for the sum of the interior angles of any polygon?

A

(N-2)180= sum of the interior angles of a polygon

Where n is equal to the number of sides a polygon contains

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19
Q

What is the sum of an interior angle and an exterior angle?

A

180

Because together they form a straight line

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20
Q

What is the sum of the exterior angles of a polygon ?

A

360

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21
Q

What is a diagonal ?

A

Any line within a polygon that extends between two vertices but is not a sideshow

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22
Q

What is the formula for the number of diagonals

A

[n(n-3)] / 2

Where n= the number of sides in the polygon

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23
Q

Why should you always label the interior angles of a polygon?

A

The angles of a polygon always add to a fixed sum

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24
Q

When visualizing shapes it is important to…?

A

Recognize every possible shape

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25
Q

When working with angles be sure to watch out for …

A

The shape that has all of its angles defined as it is usually key to solving the problem

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26
Q

Exterior angles are equal to the sum of …

A

Their two opposite interior angles

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27
Q

When there are multiple shapes always choose which one?

A

The one in which all angles are labeled

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28
Q

What is the side opposite a right angle in a right Triangle

A

Hypotenuse

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29
Q

What are the three sides of a right triangle called?

A

Hypotenuse, leg , leg

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30
Q

What is the measurement of each of the three angles in an equaltiral triangle

A

60 degrees

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31
Q

What do you know about an isosceles triangle ?

A

It has two sides of equal length

The angles opposite the equal legs of an isosceles triangles are also equal

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32
Q

What is the pythagorean theorem?

A

a^2 + b^2 = c^2

Only used for right triangles

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33
Q

How do you solve a sexy pythagorean ( right triangle w long legs ) problem?

A

x^2 - y^2 = (x+y)(x-y)

Make the unknown side
x^2= c^2 - b^2 = (c + b) (c-b)

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34
Q

What are some examples of common pythagorean triples?

A

3-4-5 [6-8-10, 9-12-15, 12-16-20 , 15, 20, 25]

5-12-13 [10-24-26]

8-15-17

7-24-25

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35
Q

What do you call a right triangle that has two angles or sides of equal measure

A

Right isosceles

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36
Q

What are the angle measurements of a right isosceles triangle

A

90 , 45 , 45

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37
Q

What are the ratios of the sides of a right isosceles triangle?

A

x: x : x(sq rt 2)

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38
Q

What is the short cut to determining the legs of a right isosceles triangle if the hypotenuse is not written as x sqr rt 2

A

Divide it by 2
Multiply it by sqr rt 2

I.e. if c = 10
Legs = 5 sqr rt 2

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39
Q

What is the ratio of the lengths of the legs of every 30-60-90 triangle?

A

x : x sqr root 3 : 2x

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40
Q

If the length of the hypotenuse of a right triangle doubles the length of one of its legs then it is a ….

A

30-60-90 triangle

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41
Q

Two 30-60-90 triangles make …

A

An equilateral triangle

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42
Q

Twelve 30-60-90 triangles make up

A

A hexagon

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43
Q

Every right triangle in a problem is usually

A

A special right triangle

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44
Q

What is the correlation between the sides and angles of a triangle?

A

The smallest angle of any triangle is always across from the smallest side

The largest angle of any triangle is always across from the largest side

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45
Q

If two angles are equal the…

A

The opposite sides are equal

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46
Q

What is the triangle inequality theorem

A

For a triangle to exist, The length of a given side must be less than the sum of the other two sides but greater than the difference between those two sides

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47
Q

What are the characteristics of a similar triangle?

A

Equal angles
Or
Proportional sides

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48
Q

What are the corollaries of similar triangles ?

A

If 2 angles of any 2 triangles are equal, the third angle must be as well

If the angles of any 2 triangles are equal, the sides of those triangles are proportional

If the sides of any 2 triangles are proportional, the angles of those triangles are equal

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49
Q

What is the advanced trick for similar triangles when it comes to area ?

A

The ratio of the areas of two similar triangles is equal to the square of the ratio of the corresponding sides

I.e. if a triangle is two times as big as another its area will be 2^2 or 4 times as large as its similar triangle

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50
Q

What is the formula for area of a triangle ?

A

(1/2) X Base X Height

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51
Q

Whats another’s name for height

A

Altitude

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52
Q

How can you calculate the area of an oddly shaped triangle w/o a clear base or height?

A

Consider rotating the triangle so that it has a defined horizontal base

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53
Q

… of a triangle is defined as the side that runs perpendicular to the height

A

Base

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54
Q

…of a triangle is defined as the perpendicular distance from a vertex to the side opposite that vertex

A

Height (altitude)

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55
Q

Advanced note…

A

The area of a triangle with sides x and y gets larger as the angle between legs x and y gets closer to 90 degrees

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56
Q

What is an exterior angle?

A

Any angle formed by extending a side of a triangle .

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57
Q

The addition of an interior angle and an exterior angle is…

A

180 degrees

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58
Q

An exterior angle is equal to the sum of its …

A

Two opposite interests angles

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59
Q

What does a triangle with parallel lines signify ?

A

Similar triangles

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60
Q

If a larger right triangle is split into two smaller tight triangles then…

A

All three triangles are similar

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61
Q

If the hypotenuse doubles the leg you are working with a … special right triangle

A

30-60-90

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62
Q

Diagonals of a rhombus always cross at what degree?

A

90

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63
Q

If two sides of a triangles are the same then ?

A

There corresponding angles are the same

64
Q

If you are trying to maximize the area of a triangle you should?

A

Make it a right triangle

If possible make it a right isosceles triangles

65
Q

What happens when you cut an equilateral triangle in half?

A

You get two 30-60-90 triangles

66
Q

In terms of triangles, what is a hexagon made of?

A

6 equilateral triangles

67
Q

What is the ratio of perimeter and area for similar triangles ?

A

The ratio of the area is the square of the ratio of the perimeters

68
Q

One big right triangle cut into two right triangles makes for …

A

Two right triangles that are proportional (similar) to the larger 1

69
Q

Anytime there is a parallel line drawn in a triangle there is a ?

A

Pair of similar triangles

70
Q

What is the sum of the interior angles of a quadrilateral?

A

360

71
Q

What are the five special quadrilaterals

A 
Rectangles 
Squares 
Rhombuses 
Trapezoids 
parallelograms
72
Q

This is a quadrilateral with opposite sides of equal lengths and 4 90 degree angles

A

Rectangle

73
Q

Describe the diagonals of a rectangle

A

They are equal
They cut each other into 4 equal halves
Do NOT intersect one and other at 90 degree angles
Do NOT bisect the corner angles of a rectangle

74
Q

A square is made up of what triangles?

A

Four 45-45-90 triangles

75
Q

Describe the diagonals of a square

A

They are equal
They intersect at a 90 degree angle
They bisect the corner angles

76
Q

What is the formula for the area of a rectangle and square?

A

Length x width

77
Q

A rhombus can be described as an?

A

Equilateral parallelogram

Slanted squares

78
Q

What do you call a slanted quadrilateral whose opposite sides are parallel and equal in length?

A

Parallelogram

79
Q

Do the diagonals of parallelograms and rhombuses bisect each other ?

A

Yes

80
Q

Are the bisections of parallelograms and rhombuses equal in length?

A

No

81
Q

The diagonals of a rhombus split it into?

A

4 right triangles as they meet at 90 degree angles

82
Q

What are the angle rules for parallelograms and rhombuses?

A

Opposite angles are equal

Adjacent angles add up to 180

83
Q

What is the formula for area of a parallelogram and a rhombus ?

A

Base x height

84
Q

What is the formula for area of a rhombus

A

(Diagonal 1 x Diagnol 2 )/2

85
Q

A quadrilateral with one set of opposing sides that are parallel but unequal in length?

A

Trapezoid

86
Q

What is the formula for area of a trapezoid ?

A

[(Base 1 + Base 2) / 2 ] x height

87
Q

To maximize the area of any quadrilateral what shape should you make it?

A

A square

88
Q

How do you minimize the perimeter of a quadrilateral? What shape should you use?

A

A square

89
Q

What should you remember about angles of rhombuses and parallelograms ?

A

Opposite angles are equal and adjacent angles add up to 180

90
Q

Is a square a parallelogram?

A

No because its sides aren’t slanted

91
Q

A diameter of a circle must do what ?

A

Pass through the center of a circle
Be twice the length of a radius
Touch two points of a circle

92
Q

What is a chord?

A

Straight line drawn from one point on a circle to another

93
Q

What is a tangent?

A

Straight line drawn outside a circle that intersects the circle at a single point

94
Q

What is the longest possible chord of a circle?

A

Diameter

95
Q

What is to be known about a chord that runs perpendicular to a radius?

A

It will be bisected by that radius

96
Q

What is to be known about a radius that is drawn to a point of tangency?

A

It intersects the tangent at 90 degrees

97
Q

What is the formula for area of a circle?

A

Pi r squared

98
Q

What is the formula for a circumference of a circle?

A

2 pi r

Or

Pi d

99
Q

What should you use when a question ask you to approximate the circumference or area of a circle

A

Approximate pi as

3 or (22/7)

100
Q

What is a portion of the circumference of a circle called?

A

An arc

101
Q

What is the portion of the area of a circle known as?

A

Sector

102
Q

What us a major arc?

A

It is an arc greater than half the circumference of a circle

103
Q

What is a minor arc?

A

An arc that is smaller than half the circumference of a circle

104
Q

What is needed to find the length of an arc?

A

Circumference and central angle

105
Q

What is the formula for length of an arc?

A

2 pi r * (x/360)

106
Q

All sectors must…?

A

Extend from the center of the circle

107
Q

What is the formula for area of a sector?

A

Pi r squared * (x/360)

108
Q

What is an inscribed angle?

A

Any angle whose vertex lies on the perimeter of a circle

109
Q

What are the three properties of inscribed angles in circles?

A

The inscribed angle of an arc is always half the measure of its central angle

Inscribed angles drawn to the same arc have equal measures

Inscribed angles of equal measure have arcs of equal length, and arcs of equal length have inscribed angles of equal measure

110
Q

What are the two properties for inscribed and circumscribed polygons?

A

An inscribed or circumscribed polygon always has the same center as the circle it inscribes or about which it is circumscribed

If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle then that triangle is always a right triangle

111
Q

What should you always do when working with circles ?

A

Label your radii

112
Q

All radii in the same circle have the same…?

A

Length

113
Q

What is the surface area of a cylinder formula?

A

2pirh + 2(pir^2)

Remember its circumference of a circle time height + 2( area of a circle)

114
Q

How do you calculate the surface area of a band of a cylinder?

A

2pir*h

115
Q

What is the highest point of the cone?

A

Apex

116
Q

What makes a cone a right circular cone?

A

The highest point runs perpendicular to it its base

117
Q

What do you call half of a sphere

A

A hemisphere

118
Q

What is there to know about the cross sections of a sphere?

A

They are circles

The closer the cross section is to the middle of a sphere the larger it is

119
Q

What is a 3-D figure w triangle sides and a polygon base?

A

Pyramid

120
Q

How do you solve any problem in which the specific dimensions of a 3D shape are unquantified

A

Pick numbers that would fit the formula and give you the answer for whats given

121
Q

What volume question should you be aware of ?

A

A volume question asking how many 3d figures can fit inside another

The answer is : UNkNOWN

You must know the exact dimensions of each shape

122
Q

How do you calculate the volume of a cylinder ?

A

Area of a circle times height

123
Q

How do you calculate slope?

A

Slope= (y2-y1)/(x2-x1)

I.e. the difference between y-coordinates over the difference in x coordinates

124
Q

What is an intercept?

A

Any point where a line intersects a coordinate axis

125
Q

When working with coordinate geometry it is critical that….

A

Every equation be rewritten in the form of y=mx+b

126
Q

What is the y intercept of equation such as y=3x

A

0,0

127
Q

What is the slope of an equation such as y=x +2

A

1

128
Q

How do you find the x intercept of a line ?

A

-b/m

Or plug 0 in for y and solve for x

129
Q

Whats a quick way to find the x or y intercept?

A

Plug 0 in for x to find the y intercept

Plug 0 in for y to find the x intercept

130
Q

How do you graph linear inequalities?

A

Put the equation in y=mx + b form

Pick a point (its easy to pick 0,0) to plug into the inequality

If the statement is true shade the side of the line that contains the point , if its false shade the side that doesnt contain that point

131
Q

Whats the slope of a horizontal line ?

A

0

132
Q

Whats the slope of a vertical line ?

A

Undefined

133
Q

What is the equation form for a horizontal line?

A

Y=b

134
Q

Whats the slope of a vertical line ?

A

Undefined

135
Q

What is the equation of a vertical line ?

A

X= a

Where a is the x intercept

136
Q

What is important to remember about parallel lines?

A

They do not intersect

They have the same slope

137
Q

What is important to remember about perpendicular lines?

A

They intersect at a 90 degree angle

The slopes of two perpendicular lines are opposite reciprocals i.e. their product is -1

138
Q

How do you find the distance between two points ?

A

Find the slope of the line So you know the rise and run

In vision a right triangle and the line is the hypotenuse

Sketch out the two legs to determine the hypotenuse using Pythagorean theorem or special right triangle knowledge

139
Q

How do you find the midpoint of two coordinates ?

A

The average of the x and y coordinates

[(x1+x2)/2] , [(y1+y2)/2]

140
Q

How do you find the equation of a line given two points ?

A

Find the slope of the line

Then plug any of the given points into y=mx +b using the slope you found

Solve for b

Then you have your equation

141
Q

How can you establish whether a line and a point intersect ?

A

Plug the coordinates values of the point into the equation of the line .

If a true statement it is on the line .

If false the statement is not on the line

142
Q

How can you find the point at which two lines intersect ?

A

Set the two equations equal to each other and solve for x

Plug the value you got for x into either equation and solve for y

The x and y are your coordinates

143
Q

What should you remember About a graph that marks one point labeled , what should you look for?

A

See of the origin is a point

144
Q

What does a perpendicular bisector do?

A

Splits a line segment in half while intersecting the segment at a 90 degree angle

145
Q

If you have two points then, you can find the…?

A

Slope

146
Q

How do you find the equation of a perpendicular bisector ?

A

Determine the slope of the bisected line segment using its two points

Determine the slope of the perpendicular bisector

Plug that slope into y=mx+b

Find the y intercept of the line

Plug everything into y=mx+b

147
Q

What type of equation is typical for a parabola ?

A

A quadratic equation

148
Q

What does a positive a term in a parabolas equation tell you ?
A negative b term ?

A 
Positive = upward parabola 
Negative = downward parabola
149
Q

Whats the different parts of a parabalas equation tell you

Y=ax^2 + bx + c

A

a=slope
b= position relative to the y axis
c= y-intercept

150
Q

How do you find the x intercepts for a parabola ?

A

Set the equation equal to 0 and solve for x

151
Q

If given an equation for a parabola plug in x values so you can find points on the graph

A

…

152
Q

What type of parabola results from an equation in the following form x=ay^2 + by + c

A

A horizontal parabola

153
Q

What does the “a” in the y ^2 term tell you about a horizontal parabola ?

A

If its positive it will open to the right

If its negative it will open to the left

154
Q

What does the “c” term tell you about a horizontal parabola ?

A

Its x intercept

155
Q

How do you find the y intercepts of a horizontal parabola?

A

Set the equation equal to 0 and solve for y

156
Q

Whats a convex polygon?

A

A polygon in which each interior angle has a measure less than 180

Gmat (18 decks)

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