Geometry Flashcards
1
Q
acute angle
A
острый угол меньше 90 градусов
2
Q
right angle
A
прямой угол
3
Q
obtuse angle
A
тупой угол 90< x< 180
4
Q
straight angle
A
угол 180 градусов
5
Q
supplementary angle
A
смежный угол, sum of two angles is 180
6
Q
complementary angle
A
if the sum of two angles is 90
7
Q
polygon
A
многоугольник
8
Q
triangle
A
треугольник
9
Q
quadrilateral
A
четырехугольник
10
Q
pentagon
A
пятиугольник
11
Q
hexagon
A
шестиугольник
12
Q
sum of interior angle measure of polygon
A
180*(n-2)
13
Q
altitude
A
высота в треугольнике
14
Q
Triangle. Supplementary angle is
A
is equal to the sum of the other angles
15
Q
Triangle. The longest side
A
The longest side is opposite the largest angle; the shortest is opposite the smallest angle
16
Q
Triangle.
A
The sum length of any two sides is greater than the length of third side
17
Q
Triangle. Area
A
S=1/2 Base X altitude
18
Q
scalene triangle
A
having no sides equal
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
- All sides are equal
- Angels = 60
- The intersection point of the altitudes is the centre circumscribed curcle about triangle and the center inscribed circle in triangle
- R: r = 2: 1 (соотношение радиусов вписанной и описанной окружностей)
- 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
Right Triangle. 45-45-90 right triangle, the leg sides
C- гипотенуза
| корень из (2)/2 - оставшиеся стороны
26
Similar Triangles.
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
Equal Triangles
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
Parallelogram
```
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
Rectangle.
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
Rhombus
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
Square
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
Trapezoid
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
Circle.
Circumference = 2*pi*R,
Area = pi*R^2
The length of the arc = 2*pi*R * X/360 (X - угол)
Area of the sector = pi*R^2*X/360 (X - угол)
pi=3.14
34
Circle. Angles
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
Circle. Inscribed and curcumscrubed
if each vertex of a polygon lies on a circle. then the polygon is inscribed.(вписанный)
Circubscrbied (описанный)
36
Hexagon
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
Rectangular solid
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
Cube
all edges are equal
V=a^3
S=6*a^2
d=a*sqroot(3)
39
Cylinder
V=pi*r^2*h
total surfaces area:
2pi*R*h (surface area of the side of a cylinder) + 2*pi*R^2
40
Coordinate plane
I quadrant справа вверху
II quadrant слева вверху
iii quadrant слева вниз
iv quadrant справа внизу
41
Distance between two points
B(X2,y2) A(x1,y1,)
| D=sqroot( (x2-x1)^2 + (y2-y1)^2) )
42
Midpoint
Xo=(X1+X2)/2
| Yo=(Y1+Y2)/2
43
Slope
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
Parabola
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
Ромб - признаки
Если в параллелограмме диагонали взаимно перпендикулярны, то этот параллелограмм — ромб.
Если в параллелограмме диагонали являются биссектрисами углов, то этот параллелограмм — ромб.
