Geometry and trigonemtry Flashcards
Kite
- Two pairs of equal sides
- One pair of equal angles
- The diagonals bisect at right angles
Rhombus
- Four sides of equal length
- Two pairs of equal angles
- Opposite sides are parallel
- The diagonals bisect each other at right angles
Radius
The distance from the edge to the centre of a circle
Chord
A straight line joining two points on the circumference of a circle
Diameter
The distance from one side of a circle to the other through the centre
Circumference
The distance around the circle/The perimeter of a circle
Tangent
A straight line which touches the edge of a circle once
Arc
A part of the circumference of a circle
Sector
An area enclosed by two radii and an arc
Segment
An area enclosed by a chord and an arc
Quadrilateral
A 2D shape with four sides
Equilateral triangle
3 sides of equal length and 3 equal angles
Right-angled triangle
A triangle that has a right angle
Isosceles triangle
2 sides of equal length and the angles at the base of the equal sides are equal
Cyclic quadrilateral
A quadrilateral drawn inside a circle where every corner of the quadrilateral touches the circumference of the circle
Sum of the interior angles of a polygon
180*(n-2)
The exterior angles of a regular polygon
360/n
The interior angles of a regular polygon
(180*(n-2))/n
a2+b2
c2
sin
opposite/hypotenuse
cos
adjacent/hypotenuse
tan
opposite/adjacent
sin(0)
0
cos(0)
1
tan(0)
0
sin(30)
1/2
cos(30)
root(3)/2
tan(30)
root(3)/3
sin(45)
root(2)/2
cos(45)
root(2)/2
tan(45)
1
sin(60)
root(3)/2
cos(60)
1/2
tan(60)
root(3)
sin(90)
1
cos(90)
0
tan(90)
Undefined
Area of a triangle
(1/2)ab*sin(C)
Area of a parallelogram
base*height
Area of a trapezium
(1/2)(a+b)h
Arc length
(angle/360)*2πr
Sector area
(angle/360)*πr2
Face
A flat surface
Edge
Where two faces meet
Vertex
A corner where edges meet
Volume of a cuboid
lengthwidthheight
Volume of a prism
area of the cross-section*length
Volume of a cylinder
πr2*h
Surface area of a cylinder
2πr2+2πrh
Volume of a cone
(1/3)πr2h
Surface area of a cone
πr2+πrh
Volume of a sphere
(4/3)*πr3
Surface area of a sphere
4πr2
1l
1000cm3
Length scale factor
k
Area scale factor
k2
Volume scale factor
k3
How do you know if two figures are similar?
Their angles are equal and their sides are in proportion
How do you prove two triangles are similar?
- Side Side Side (SSS)
- Angle Angle (AA)
- Side Angle Side (SAS)
