Geometry Flashcards
Pythagoras theorem (dont need to learn)
A(sq) + b(sq) = c(sq)
Bearing rules
1) find the word from in the question, and put your pencil on the diagram at the point you are going ‘from’
2) at the point you are going from, draw a northline
3) now draw in the angle clockwise from the northline to the line joining the two points, this angle is the required bearing
SohCahToa
Sine (opp, hyp) , cos (adj, hyp) , tan (opp, adj)
Cosine rule (dont need to learn)
a(sq) = b(sq) + c(sq) - 2bc cosA
Cosine rule for angle
CosA = b(sq) + c(sq) - a(sq) /2bc
Sine rule (dont need to learn)
a/sinA = b/sinB = c/sinC
3D pythagoras
In a cuboid/cube/pyramid
1) draw a right angled triangle from the points needed, either to find the length or the angle
2) draw the triangle separately from the diagram and clearly label it
3) use pythag for the missing lengths then use shift and trig for the angle
Radius
Straight line from the centre to the circumference of a curcle
Circumference
The length around the whole circle
Diameter
A straight line that touches the circumference in 2 places and passes through the centre
Chord
A straight line that touches the circumference in 2 places but doesn’t go through the centre
Sector
A slice of the circle trapped between 2 radii
Arc
A curved line which is a section of the circumference
Segment
An area of the circle trapped between a chord and the circumference
Tangent
A straight line that touches the circumference exactly once
Circumference equation for a circle (dont need to learn)
PiD / 2piR
Area equation of a circle (dont need to learn)
PiR(sq)
Arc length equation
x/360 x 2piR
Sector area equation
x/360 x piR(sq)
Area of a triangle
1/2 x b x h
Alternative equation for a triangle (dont need to learn)
1/2 a b sinc
Area of a parallelogram
B x h
Area of a trapezium (dont need to learn)
1/2 x (a+b) x h
Surface area is
The total area of all the outer surfaces added together
Surface area of a sphere (dont need to learn)
4 pi r(sq)
Surface area of a cone
Pi r l + pi r(sq)
Surface area of a cylinder
2 pi r h + 2 pi r(sq)
Volume of a cuboid
L x W x H
Volume of a sphere (dont need to learn)
4/3 pi r (cbd)
Volume of a cone (dont need to learn)
1/3 x pi r (sq) x h
Volume of a prism (dont need to learn)
Cross sectional area x length
Volume of a pyramid
1/3 area of base x height
Curved surface area of a cone (dont need to learn)
pi r l
Total SA of a cone
Pi r l + pi r (sq)
Volume of a cylinder (dont need to learn)
Pi r(sq) h
Volume of a hemisphere
1/2 x 4/3 pi r(cb)
Surface area of a hemisphere
2 pi r(sq)
Total surface area of a hemisphere if solid
Pi r(sq) + 2 pi r(sq)
Curved surface are of a cylinder (dont need to learn)
2 pi rh
alternate angles look like
Z
corresponding angles look like
F
interior angles (C) add up to
180 degrees
