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Bryx_Math > Plane Geometry > Flashcards

Plane Geometry Flashcards

1
Q

Book of Euclid which given emphasis on Plane Geometry

A

Elements

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2
Q

Branch of Geometry that deals with plane figure or geometrical shapes of two dimensions

A

Plane Geometry

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3
Q

Branch of Geometry deals with properties of geometrical shapes of three dimensions such as cones, pyramids, cylinders

A

Solid Geometry

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4
Q

Branch of Geometry based on the assumptions of Euclid

A

Euclidean Geometry

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5
Q

Branch of Geometry that is not based on the assumption of Euclid

A

Non-Euclidean Geometry

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6
Q

Branch of Geometry that deals with the study of those properties of plane figures that are unchanged when given set of points is projected onto a second plane

A

Projective Geometry

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7
Q

Branch of Geometry which specializes on the study of triangle

A

Trigonometry

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8
Q

Branch of Geometry that deals with geometric problems by using the coordinate systems and transforming them into algebraic problems

A

Analytic Geometry

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9
Q

Branch of Geometry that applies differential and integral calculus to curves, surfaces and other geometric entities

A

Differential Geometry

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10
Q

What are the 5 basic postulate of Euclid?

A
  1. A unique line can be drawn between any two points
  2. Such line can be extended indefinitely in either direction
  3. A circle can be drawn in a plane using a given point (a center) and a given distance(a radius)
  4. All right angles are equal
  5. Given a line and a point not on the line, there exist exactly one line parallel to the original line passing through the given point (aka parallel postulate)
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11
Q

A dimensionless geometric figure having no properties other than location or place

A

Point

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12
Q

The shortest distance between any two points.

A

Line

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13
Q

The opening between two lines or planes that meet

A

Angle

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14
Q

What is a straight angle?

A

Equal to 180 degrees or (pi) radians

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15
Q

What is a reflex angle?

A

Greater than 180 degrees but less than 360 degrees

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16
Q

What is a Full angle or Perigon?

A

Equal to 360 degrees or 2*pi radians

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17
Q

Two angles with a common leg

A

Adjacent angles

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18
Q

Two angles where the sum is a right angle

A

Complementary Angles

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19
Q

Two angles where the sum is a straight angle (180degrees)

A

Supplementary angles

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20
Q

Two angles whose sum is a perigon

A

Explementary angles

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21
Q

Angles formed by two intersecting lines

A

Vertical Angles

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22
Q

It is a unit of angle based on sexagesimal system

A

Degree

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23
Q

Standard angular measure in international system of units

A

Radian

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24
Q

It is a measure ofan angle which is 1/6400 of the full circle

A

Mil

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25
Q

1 Revolution in terms of Gon

A

400

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26
Q

1 Revolution in terms of Mil

A

6400

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27
Q

Number of sides of regular Hectagon

A

100

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28
Q

Number of sides of a regular Megagon

A

10^6

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29
Q

Number of sides of a regular googolgon

A

100^100

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30
Q

How many sides does Undecagon have?

A

11

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31
Q

How many sides of Dodecagon

A

12

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32
Q

It is the inward pointing angle of the concave polygon

A

Reentrant angle

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33
Q

Other angles of a concave polygon except the Reentrant angle

A

Salient Angle

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34
Q

it is the line connecting two opposite vertices

A

diagonal

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35
Q

Number of diagonals formula

A

No. of Diagonals=(n/2)*(n-3)

where n=number of sides

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36
Q

formula of sum of interior angles

A

(n-2)*180degrees

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37
Q

It is the angle subtended by the prolongation of one side to the next

A

deflection angle

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38
Q

The sum of all deflection angle equals to?

A

360 degrees

39
Q

A triangle where all sides are equal

A

Equilateral Triangle

40
Q

A triangle where two sides are equal

A

Isosceles Triangle

41
Q

A triangle where no two sides are equal

A

Scalene Triangle

42
Q

Each interior angle is less than a right angle

A

Acute triangle

43
Q

One angle is a right angle

A

Right triangle

44
Q

One angle is greater than right angle

A

Obtuse triangle

45
Q

A triangle which is not a right triangle is called what?

A

Oblique Triangle

46
Q

A triangle with 3,4,5 units

A

Egyptian Triangle

47
Q

A triangle inscribed in a given triangle whose vertices are the feet of the three perpendicular to the sides from some points inside a given Triangle

A

Pedal Triangle

48
Q

An isosceles triangle with sides is to its base in the golden ratio; its angles are 72,72 and 36 degrees

A

Golden Triangle

49
Q

What is a rhombus?

A

A type of quadrilateral with all sides are equal but no angle equal to right angle

50
Q

What is a parallelogram?

A

Both pairs of opposite sides are parallel.

51
Q

What is another term for a parallelogram?

52
Q

A quadrilateral wherein only two sides are parallel

53
Q

A quadrilateral where no two sides are parallel

54
Q

What is a Kite quadrilateral?

A

A convex quadrilateral whose adjacent sides are equal in pair

55
Q

What is a deltoid quadrilateral?

A

A concave quadrilateral whose adjacent sides are equal in pair

56
Q

It is a quadrilateral whose vertices lie on a circle

A

Cyclic quadrilateral

57
Q

Area of a rhombus

A

A=bh
where b=base
h=height

58
Q

Area of rhombus given two diagonals

A

A=(1/2)d1*d2

59
Q

Are of rhombus given a side and included angle

A

A=a^2(sin(theta))

60
Q

Area of parallelogram given base and altitude

61
Q

Area of parallelogram given two diagonals and included angle

A

A=(1/2)d1d2sin(theta)

62
Q

Area of parallelogram given two sides and an interior angle

A

A=ab*sin(theta)

63
Q

Area of a trapezoid

A

A=1/2(B+b)*h
where B=length of upper base
b=length of lower base
h=height

64
Q

Area of a Trapezium (General Quadrilateral)

A

A=1/2(d1d2)*sin(theta)

where d1 and d2 are the lengths of diagonal

65
Q

Area of a general quadrilateral given four sides and opposite angles

A

A=sqrt((s-a)(s-b)(s-c)(s-d)-abcd(cos^2(theta)))
theta=(A+C)/2 or (B+D)/2
s=(a+b+c+d)/2

66
Q

Area of a cyclic quadrilateral

A

A=sqrt((s-a)(s-b)(s-c)*(s-d))

A=sqrt((s-a)(s-b)(s-c)*(s-d

67
Q

radius of the circle circumscribing the quadrilateral Formula

A

r=(sqrt((ab+cd)(ac+bd)(ad+bc)))/(4A)

68
Q

Area of quadrilateral circumscribing a circle

A

A=rs=sqrt(abcd)

where s=(a+b+c+d)/2

69
Q

Area of a regular polygon

A

A=(1/4)*(na^2)cot(180/n)
where a=length of side
n=number of sides

70
Q

Perimeter of a regular polygon

A

P=na
where a=length of side
n=number of sides

71
Q

Area of a regular polygon circumscribing a circle

A

A=nr^2tan(180/n)

72
Q

Perimeter of a regular polygon circumscribing a circle

A

P=2nr*tan(180/n)

73
Q

Area of a regular polygon inscribed in a circle

A

A=(1/2)*nr^2sin(360/n)

74
Q

Perimeter of a regular polygon inscribed in a circle

A

P=2nr*sin(180/n)

75
Q

It is the length of a circle between two points on the circle

76
Q

a line touching the circle at one point. It is also perpendicular to the radius of the circle

77
Q

A line cutting the circle in two place

A

Secant of a circle

78
Q

It is the longest chord of a circle that passes through the center

79
Q

Distance from the center to the circle

80
Q

the segment of a secant bounded by the circle

81
Q

Area bounded by two radii and the included arc

A

Sector of a circle

82
Q

Area bounded by a chord and the arc subtending the chord

83
Q

An angle whose vertex is at the center of a circle and whose sides are the radii

A

Central Angle

84
Q

An angle whose vertex is along the periphery or circumference and its sides are the chords

A

Angle subtended by the chord

85
Q

Are of sector of a circle

A 
A=(1/2)*(rc)
A=(1/2)*(r^2*theta)
r=radius
c=arc length
theta=central angle
86
Q

Area of segment of a circle

A

A=A(sector)-A(triangle AOB)

87
Q

If a central angle and a peripheral angle are subtended by the same arc, then the central angle is ________ as large as the peripheral angle

88
Q

What is the relationship of the inscribed angles subtending the same arc?

89
Q

Inscribed angles subtended by the diameter of a circle are ______ angles

A

right angles (90 degrees)

90
Q

What is the chord theorem formula?

91
Q

What is the secant theorem formula?

A

a(a+b)=c(c+d)

92
Q

What is Secant-Tangent theorem formula?

A

t^2=a*(a+b)

93
Q

Area of an ellipse formula

94
Q

it is a general term for all angles that lie on a plane surface

A

plane angle

Bryx_Math (9 decks)

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