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Geometry > fi > Flashcards

fi Flashcards

1
Q

ways to determine a plane

A

3 noncolinear points

a line and a point not on the line

2 intersecting lines

2 parallel lines

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2
Q

if a line intersects a plane not containing it…

A

then the intersection is exactly one point

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3
Q

if 2 planes intersect…

A

their intersections is exactly one line

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4
Q

If a line is perpendicular to 2 lines thru the foot…

A

then it is perpendicular to the plane

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5
Q

If a line is perpendicular to a plane…

A

then it is perpendicular to every line thru the ft

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6
Q

a line is perpendicular to a plane if…

A

it is perpendicular to every one of the lines that pass thru its ft

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7
Q

A line and a plane are parallel if…

A

they do not intersect

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8
Q

two planes are parallel if…

A

they do not intersect

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9
Q

what are skew lines

A

non-coplanar, non-parallel lines

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10
Q

T/F: if a plane contains one of two skew lines, it contains the other

A

False

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11
Q

T/F: If a line and a plane never meet, they are parallel

A

true

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12
Q

T/F: If two parallel lines lie in different planes, the planes are parallel

A

False

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13
Q

T/F: If a line is perpendicular to two planes, the planes are parallel

A

true

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14
Q

T/F: If a plane and a line not in the plane are each perpendicular to the same line, they are parallel to each other

A

True

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15
Q

the measure of an exterior angle of a triangle is equal to

A

the sum of the measure of the remote interior angles

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16
Q

a segment joining the midpoints of 2 sides of triangle is…

A

parallel to the 3rd side and its length is 1/2 the length of the third side

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17
Q

If 2 angles of one triangle are congruent to 2 angles of a second triangle…

A

then the 3rd angles are congruent

(AKA NO CHOICE THEOREM)

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18
Q

pentagon

A

5 sides

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19
Q

hexagon

A

6 sides

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20
Q

heptagon

A

7 sides

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21
Q

octagon

A

8 sides

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22
Q

nonagon

A

9 sides

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23
Q

decagon

A

10 sides

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24
Q

dodecagon

A

12 sides

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25
Q

pentadecagon

A

15 sides

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26
Q

n-gon

A

number

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27
Q

regular polygon is

A

equilateral and equiangular

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28
Q

1 3
x a
— = —
y b

2 4

what are the means and what are the extremes

A

numbers referring to terms

means: 2nd and 3rd
extremes: 1st and 4th

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29
Q

if the product of a pair of non-zero numbers is equal to the products of another pair of non-zero numbers then…

A

either pair of numbers may be made the extremes and the other pair the means of a proportion

JUST REFER TO THE SLIDE SO THIS MAKES SENSE

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30
Q

corresponding angles of similar triangles are…

A

congruent

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31
Q

coresponding sides of similar triangles are…

A

proportional

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32
Q

the altitude is drawn to the hypotenuse of a right triangle then…

A

3 similar triangles are produced

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33
Q

concentric circles

A

share the same center

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34
Q

congruent circles

A

circles are congruent if they have congruent radii

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35
Q

chord

A

segment that joins any 2 points on the circle

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36
Q

diameter

A

chord that goes through the center of the circle

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37
Q

if a radius is perpendicular to a chord then…

A

it bisects the chord

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38
Q

If a radius of a circle bisects a chord then…

A

is it perpendicular to that chord

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39
Q

If a line is the perpendicular bisector of a chord then…

A

it passes through the center of the circle

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40
Q

If a line is the perpendicular bisector of a chord, then…

A

it passes through the center of the circle

41
Q

If 2 chords of a circle are equidistant from the center, then…

A

they are congruent

42
Q

If 2 chords of a circle are congruent, then…

A

they are equidistant from the center of the circle

43
Q

minor arc

A

less than 180

44
Q

major arc

A

greater than 180

45
Q

central angle measure is equal to

A

the arc

46
Q

what makes arcs congruent

A

equal length

47
Q

If central angles congruent then arcs congruent then chords congruent

A

MEMORIZE THAT ^

48
Q

measure of an arc from a fractional part

A

fraction times 360

49
Q

secant

A

a line that intersects a circle at 2 points

50
Q

tangent

A

a tangent line is perpendicular to the radius drawn to the point of tangency

51
Q

tangent

A

*a line that intersects the circle at one point

a line perpendicular to the radius drawn to the point of tangency

if a line if perpendicular to a radius at its outer endpoint then it is tangent

52
Q

tangent segment

A

only intercept one point

53
Q

secant segment

A

has internal and external segments that make up one secant

54
Q

if 2 tangent segments are drawn to a circle from an external point then…

A

those segments are congruent

55
Q

internal common tangent

A

in between two circles

56
Q

external common tangent

A

outside the 2 circles

57
Q

external common tangent

A

outside the 2 circles

58
Q

an inscribed angle is

A

half the measure of the arc

59
Q

chord-chord angle

A

arc + arc/2

60
Q

secant-secant angle, secant tangent angle, tangent, tangent angle

A

outer arc-inner arc/2

61
Q

if 2 inscribed or tangent chord angles intercept the same arc, then…

A

they are congruent

62
Q

tangent-tangent angle and its minor arc is 180

A

1/2(180-x)

63
Q

inscribed angle meaning…

A

all vertices are on the circle

64
Q

circumscribed

A

all sides are tangent to the circle

65
Q

If a parallelogram is inscribed in a circle, it…

A

has to be a rectangle

66
Q

the length of an arc is = to the circumference of it circle times the fractional part of the circle determined by the arc

A

is = to the circumference of it circle times the fractional part of the circle determined by the arc

67
Q

a median of a triangle

A

divides the triangle into 2 triangles with equal areas

68
Q

AAS

A

Angle angle side in this order to prove two triangles congruent

69
Q

sum of the measures of angles in a polygon

A

(n-2) x 180

the n is referring to the number of sides

70
Q

exterior angles of a polygon always equal…

A

360 degrees

71
Q

number of diagonals in a polygon that can be draw in polygon is given by….

A

n(n-3)/2

72
Q

each exterior angle measure is given by

A

E = 360/n

73
Q

meaning of similar figures

A

same shape not same size
measures are equal

74
Q

ways to prove similar triangles

A

AA, SSS, SAS

75
Q

If a line is parallel to one side of a triangle and intersects the other sides it,

A

divides the 2 sides proportionally

LOOK AT NOTES

76
Q

If 3 or more parallel lines are intersecting by 2 transversals,

A

the parallel lines divide transversals proportionally

LOOK AT NOTES

77
Q

If a ray bisects an angle of a triangle,

A

it divides the opposite side into segments that are proportional to adjacent sides

LOOK AT NOTES

78
Q

distance formula

A

square root of (x1 - x2)^2 + (y1-y2)^2

79
Q

pythagorean triples

A

3-4-5
6-8-10
7-24-25
5-12-13
8-15-17

80
Q

If 2 inscribed or tangent-chord angles intercept congruent arcs then

A

theyre congruent

81
Q

find length of arc

A

arc (pir^2)
—
360

82
Q

area of rectangle

A

b x h

83
Q

area of square

A

s^2

84
Q

parallelogram

A

b x h

85
Q

area of triangle

A

1/2(b x h)

86
Q

area of a trapezoid

A

1/2 h (b1 + b2)

87
Q

area of a kite

A

1/2 d1 d2

88
Q

area of equilateral triangle

A

s^2/4 x root 3

89
Q

area of regular polygon

A

1/2 a p

90
Q

area circle

A

pi r^2

91
Q

find ratio is areas

A

A1/A2 = (S1/S2)^2

92
Q

hero’s area of triangle

A

square root of s(s-a)(s-b)(s-c)

semiperimeter = s

93
Q

area of cyclic quad

A

square root of (s-a)(s-b)(s-c)(s-d)

94
Q

surface area of prisms

A

LA = area of faces

TA = LA + 2B(area of bases)

V = B x h

rectangular prism = l x w x h

95
Q

surface area of cylinder

A

LA = 2pir (h)

TA: 2pir + 2(pir^2)

V = B (pir^2) x h

96
Q

surface area of pyramids

A

LA: area of faces

TA: LA + B

V = 1/3 B x h

97
Q

surface area of cone

A

LA: pi r l

TA: pi r l + pir^2

V = 1/3 B x h

98
Q

surface area of a sphere

A

TA: 4pir2

V = 4/3pir^3

Geometry (1 decks)

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