Area
the number of square units needed to cover a flat surface
Area of a Rectangle
(Base)(Height)
Area of a Right Triangle
A=½bh
Area of a Parallelogram
(Base)(Height)
Area of a Triangle
A=½bh
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
Who was the famous Indian Chief of Trig Ratios?
Chief SOHCAHTOA
Area of a Trapezoid
A=½(b1+b2)h
Area of a Rhombus
½(d₁)(d₂)
Pythagorean Theorem
a² + b² = c²
Area of an Equilateral triangle
A=¼s²√3
Semiperimeter of a Triangle
S= a+b+c/2 (ONE HALF THE PERIMETER OF A TRIANGLE)
Heron's Formula
Area = √(s-a)(s-b)(s-c)
Central Angles of a Regular n-gon
360°
ARea of a Regular Polygon
A=½ap (Where 'a' is the apothem, and 'p' is the perimeter)
Apothem of an Equilateral Triangle
1/3h (one third the length of the altitude) OR (√3)/6s
Area of a Circle
A=πr²
Surface Area of a Prism
sA= L + 2B
Lateral Surface Area of a Right Prism
LsA=pH (Where 'p' is the perimeter of the bases, and 'H' is the product of the height)
Surface Area of a Cylinder
S = L + 2B (The lateral surface area and the surface area of the bases) ..... ( sA=½pl+½ap) .....( sA=½p{l+a} )
Lateral Surface Area of a Right Cylinder
L =cH (where 'c' is the circumfrence of the bases, and 'H' is the height of the Cylinder)..... (sA=½cl+½r/c) { 'r' is the radius of a circular base, 'c' is the circumference of the base, 'l' is the slant hieght } .....{ sA=½c(l+r) }
Surface Area of a Pyramid
S =L+B (Lateral Surface area, and the area of the base)
Lateral Area of a Pyramid
L= ½pl (Perimeter of base times the slant height)
Lateral Area of a Cone
L= ½cl (Circumfrence of the base times the slant hight)
Surface Area of a Sphere
sA= 4πr²
Volume of a Regular Hexahedron (Cube)
sA= e³
Congruent Circles
Circles with congruent radii
Secant
A line in the same plane as the circle which intersects it in exactly two points
Tangent
A line in the sma plane as the circle which intersects it in exactly one point
Point of Tangency
The point where a tangent intersects a circle
Central Angle
An Angle that is in the same plane as the circle and whose vertex is in the center of the circle
Inscribed Angle
An angle whose vertex is on a circle and whose sides contain chords of the circle.
Arc Measure
The measure of the central angle that intercepts an arc, measured in degrees.
Minor Arc
An arc measuring less than 180°, denoted with two letters which are the endpoints of the arc.
Major Arc
An Arc measuring more than 180°. Major arcs are denoted with three letters of which two are the endpoints and another is a point on the arc
Semicircle
An arc measuring 180°
Congruent Arcs
Arcs ona circle that have the same measure
Sector of a Circle
A region bounded by two radii and the intercepting arc
Segment of a Circle
THe region bounded by a chord and its intercepted arc
Degree Measure of an Arc
l=cθ/360° ('θ' is the degree measure of the arc, 'l' is the length of the arc, 'c' is the circumference of the circle)
Area of a Sector
A= Acθ/360 ('A' is the are of the sector, 'Ac' is the area of the circle, and 'θ' is the arc measure in degrees)
Volume of a Solid
The number of cubic units contained in the interior of a solid.
Volume of a Cube
V= e³
Volume of a Prism
V= BH
Volume of a a Circular Cylinder
V= πr²H
Volume of a Pyramid
V=⅓bh
Volume of a Cone
Volume = ¹/₃πr²h
Volume of a Sphere
⁴/₃πr²
Transformation
One to One Function from the plane onto the plane
Reflection
A transformation that maps each point A of a plane onto the point A' such that the following conditions are met { 1) If A is on l, then A=A'; If A is not on l, then l is the perpindicular bisector of line segment AA'}
Translation
A transformation formed by the composition of two reflections in which the lines are parallel lines
Rotation
A transformation that turns a figure about a fixed point at a given angle and a given direction.
Dilation
A transformation that expands or contracts the points of the plane in relationto a fixed point, .
Isometry
A transformation that preserves distance
Line Symmetry
When each half of the figure is the image of the other half under some reflection in a line.
Rotational Symmetry
When the image of the figure coincides with the figure after a rotation. The magnitude of the rotation must be less than 360°.
Sine
ratio of the opposite side to the hypotenuse of a right-angled triangle
Cosine
ratio of the adjacent side to the hypotenuse of a right-angled triangle
Tangent
ratio of the opposite to the adjacent side of a right-angled triangle
Trigonometry
the mathematics of triangles and trigonometric functions
45-45-90
A special right triangle with two legs being x, and the hypotenuse x√2.
30-60-90
A special right triangle with one leg being x, the leg opposite the 60° angle being x√3, and the length of the hypotenuse 2x.