♥GEOMETRY FORMULAS AND DEFINITIONS♥

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.