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Quant Formulas > Geometry > Flashcards

Geometry Flashcards

1
Q

acute angle

A

острый угол меньше 90 градусов

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2
Q

right angle

A

прямой угол

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3
Q

obtuse angle

A

тупой угол 90< x< 180

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4
Q

straight angle

A

угол 180 градусов

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5
Q

supplementary angle

A

смежный угол, sum of two angles is 180

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6
Q

complementary angle

A

if the sum of two angles is 90

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7
Q

polygon

A

многоугольник

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8
Q

triangle

A

треугольник

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9
Q

quadrilateral

A

четырехугольник

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10
Q

pentagon

A

пятиугольник

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11
Q

hexagon

A

шестиугольник

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12
Q

sum of interior angle measure of polygon

A

180*(n-2)

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13
Q

altitude

A

высота в треугольнике

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14
Q

Triangle. Supplementary angle is

A

is equal to the sum of the other angles

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15
Q

Triangle. The longest side

A

The longest side is opposite the largest angle; the shortest is opposite the smallest angle

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16
Q

Triangle.

A

The sum length of any two sides is greater than the length of third side

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17
Q

Triangle. Area

A

S=1/2 Base X altitude

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18
Q

scalene triangle

A

having no sides equal

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19
Q

isosceles triangle

A

равнобедренный

20
Q

equilateral triangle

A

раносторонний

21
Q

sides of the isosceles triangle sometimes called

A

legs

22
Q

Equliateral Triangle. Properties

A
  1. All sides are equal
  2. Angels = 60
  3. The intersection point of the altitudes is the centre circumscribed curcle about triangle and the center inscribed circle in triangle
  4. R: r = 2: 1 (соотношение радиусов вписанной и описанной окружностей)
  5. Area = sqrroot(3)/4 X a^2
23
Q

Right Triangle.Pythogorean triple

A 
Pythogorean triple:
3 : 4 : 5
5 : 12: 13
8 : 15:17
7:24:25
24
Q

Right Triangle. 30-60-90 right triangle, the leg sides

A

C- гипотенуза
1/2С - против угла в 30 градусов
корень из (3)/2 = против угла в 60 градусов

25
Q

Right Triangle. 45-45-90 right triangle, the leg sides

A

C- гипотенуза

корень из (2)/2 - оставшиеся стороны

26
Q

Similar Triangles.

A

When Corresponding angles of two triangles are equal the triangles are said to be similar.
Angles are similar provided the following three conditions are satisfied:
1. all angles are equal
2. AB/A1B1 = AC/A1C1=BC/B1C1
3.AB/A1B1=AC/A1C1, angel A = A1

27
Q

Equal Triangles

A

Two triangles are equal provided the following three conditions are satisfied:

  1. AB=A1B1, AC=A1C1, BC=B1C1
  2. AB = A1B1, AC=A1C1, angel A=A1
  3. AB=A1B1, angle A=A1, angel B=B1
28
Q

Parallelogram

A 
Two Pairs of parallel sides
Properties:
1. The opposite sides are parallel:
AB||CD, AD || BC
2. The opposite sides are equal:
AB=CD, AD=BC
3. The opposite angles are equal:
angel A=C, B=D
4. The diagonals bisect each other:
AE=EC, BE=ED
5. The are of a parallelogram is equal to a side
S=A *H (высота к основанию)
6. сумма consecutive angles= 180
29
Q

Rectangle.

A

Прямоугольник. Это параллелограммам у которого углы 90 градусов.

Properties of a rectangle:
1. the diagonals are equal:
AC=BD
2. The are of a rectangle is equal to the product of length and width: S=a X b

30
Q

Rhombus

A

A parallelogram having four equal sides
Properties of a rhombus:
1. The diagonals are perpendicular:
AC parallel BD
2. The diagonals bisect the angles they join:
AC bisects angle A and C, BD bisects angle B and D
3. The are of rhombus is equal to one-half a product of the two diagonals:
S = 1/2 X d1 x d2
or S=a x h

31
Q

Square

A

parallelogram having four equal angles and four equal sides
1. The diagonals are equal: AC = BD
2. Diagonals are perpendicular : AC perpendicular BD
3. The diagonals bisect the angles they join
4. The are of a square is equal to its side squared or equal to one-half its diagonal squared:
S=a^2=1/2*d^2

32
Q

Trapezoid

A

a qudraliteral having one pair of parallel sides is called trapezoid. The parallel sides are called bases, nonparallel sides called legs.

Area:
S = 1/2 * h (b1+b2)

33
Q

Circle.

A

Circumference = 2piR,
Area = piR^2
The length of the arc = 2piR * X/360 (X - угол)
Area of the sector = piR^2*X/360 (X - угол)
pi=3.14

34
Q

Circle. Angles

A

Central angel- an angel formed by two radii of a circle is called a central angle
Inscribed angle - formed by two chords having common endpoint on the circumference of a circle

If inscribed angle and central angle intercept the same arc, the inscribed angle will measure exactly half the central angle.

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

35
Q

Circle. Inscribed and curcumscrubed

A

if each vertex of a polygon lies on a circle. then the polygon is inscribed.(вписанный)

Circubscrbied (описанный)

36
Q

Hexagon

A

Polygon having six sides.
The sum of internal angles = 720
Properties:
1. Area S = 6 * sqroot(3)/4 * a^2
2. If R is a radius of the circumscribed circle then R=a
3. if r is a radius of inscribed circle then R=sqroot(3)/2*a

37
Q

Rectangular solid

A

Three dimensional figure formed by 6 rectangular surfaces. Each recantgular surface is a face.

6 faces, 12 edges, 8 vertices and 4 diagonals.

V=a*b*c
Surfaces area:
S = 2 (a*b +b*c + a*c)
The length of a diagonal
d=sqroot(a^2+b^2+c^2)
38
Q

Cube

A

all edges are equal
V=a^3
S=6a^2
d=asqroot(3)

39
Q

Cylinder

A

V=pir^2h
total surfaces area:
2piRh (surface area of the side of a cylinder) + 2piR^2

40
Q

Coordinate plane

A

I quadrant справа вверху
II quadrant слева вверху
iii quadrant слева вниз
iv quadrant справа внизу

41
Q

Distance between two points

A

B(X2,y2) A(x1,y1,)

D=sqroot( (x2-x1)^2 + (y2-y1)^2) )

42
Q

Midpoint

A

Xo=(X1+X2)/2

Yo=(Y1+Y2)/2

43
Q

Slope

A

y=kx+b
k-slope

slope = (Y2-Y1)/(X2-X1)

Two lines L1,L2 perpendicular, k1*k2= -1, k1,k2 - slopes

The value of the slope gives the angle between the line and x-axis.

44
Q

Parabola

A

y=ax^2+bx+c - curve
parabola’s axis of symmetry: x=-b/2a
if a>0 parabola opens upward
if a<0 parabola opens downward

45
Q

Ромб - признаки

A

Если в параллелограмме диагонали взаимно перпендикулярны, то этот параллелограмм — ромб.
Если в параллелограмме диагонали являются биссектрисами углов, то этот параллелограмм — ромб.

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