Geometry

Trig, Angles, Area, Volume

angle rules (3)

• total angle in triangle = 180

• total on straight line = 180

• total angle around a point = 360

corresponding angles

equal when 2 lines parallel

alternate angles

equal when 2 lines parallel

vertically opposite angles

2 lines intersect

polygon

2D enclosed shape with straight sides

interior + exterior angle = ?

? = 180 degrees

equation to find sides from exterior angles

360 / value of one exterior angle

• degrees * n = 360

equation to find interior angles from # of sides (n)

180 * (n-2) / n = degrees

equation for total sum of interior angles

(n-2) * 180

pythagoras’ theoreom:

a²+ b²= c² (hypotenuse)

sine

sin(degrees) = opp / hyp

• opp = the side opposite to the unknown angle

cosine

cos(degrees) = adj / hyp

• adj= side next to the unknown angle

tangent

tan(degrees) = opp / adj

sin/cos/tan ^-1

uses the ratio to find the angle

• sin(degrees) uses degree to find ratio

exact trig value song

volume + area of a cone

V: 1/3 * πr² h

A: πr² + πrl

frustum

when the tip of a cone is excluded

• volume = cone - smaller cone

volume + area of a pyramid

V: base area * h / 3

A: base area + (# of faces * face area)

volume + area of a sphere

V: 4/3πr²

A: 4πr²

what is a prism?

3D object with same cross section throughout

volume + area of a prism

V: base area * length

A: (area of each face * # of each face) + 2(base area)

volume + area of a cylinder

V: πr²h

A: 2πrh(circumference + height) + 2πr² (2 faces)

labelled circle

area + circumference of an arc

A: degree/360 * πr²

C: degree/360 * 2πr

plan vs elevation

plan: birds-eye view directly from above

elevation: view from front or side

reflections

1. count squares perpendicularly to each vertex

2. plot each vertex equal distance to the opposite side

3. when going diagonally, draw lines of reflection, flip tracing paper to line up /w LoR

describing a reflection

M1: naming “reflection”

M2: naming equation for line or reflection

vectors

Top: x // Bottom: y

(+) move up or right // (-) move down or left

transformation

1. count how many times vertice must be moved

2. plot new points

describing a transformation

M1: naming “transformation”

M2: naming the vector

rotation

1. copy vertices on both sides of tracing paper

2. keep pencil on center point of rotation when turning

describing a rotation

M1: naming “rotation”

M2: naming point of rotation

M3: naming degrees of turning

M4: naming clockwise/anticlockwise

enlargement

1. count squares for distance to center of enlargement

2. plot new vertices by multiplying scale factor (distance * sf)

describing an enlargement

M1: naming “enlargement”

M2: naming center of enlargement

M3: naming SF

todo, bisectors and constructions, new trig sheet