Congruence and Similarity
Symbol for showing congruence  ≅
Symbol for showing similarity  ~
Two angles and one side = A.S.A (or) A.A.S
Two sides and one angles = S.A.S
Three sides = S.S.S
One right angle included = R.H.L (or) R.H.S
Two similar angles = A.A
Three similar sides = S.S.S
Two similar sides and one angles = S.A.S
Pythagoras Theorem
a(square) + b(square) = c(square)
Angles in Two-Dimensional figures
 = line
.----. = line segment
. = ray
supplementary = two angles add up to 180 degree
complementary = two angles add up to 90 degree
adjacent angles on a line = all angles add up to 180 degree
vertically opposite angles = four angles add up to 360 degree
three types of matching angles = corresponding, alternate, angles between parallel lines
Geometric Measurement
Polyhedron = many faces, prism and pyramid
non-Polyhedron = cylinder, cone, sphere (or) hemisphere
equations
area of square = s (square)
area of rectangle = l x b
area of triangle = ½ bh
area of circle = 𝜋 r(square)
circumference of circle = 2 𝜋 r
surface area of square based pyramid = area of square base + 4(area of triangle)
surface area of cone = 𝝅 r(square) + 𝝅 r s
surface area of cylinder = 2 𝝅 r(square) + 2 𝝅 r h
surface area of sphere = 4 𝝅 r(square)
surface area of hemisphere or hollow hemisphere = 2 𝝅 r(square)
surface area of solid hemisphere = 3 𝝅 r (square)
volume of prism = base are x height
volume of pyramid = 1/3 bh
volume of hemisphere = 2/3 𝝅 r(cube)
volume of sphere = 4/3 𝝅 r(cube)
Linear Graphs
linear equation  straight line
origin = (0,0)
general equation  y = mx + c
Coordinate Geometry
midpoint of a line segment  (x1 + x2 /2, y1 + y2 /2)
distance formula (length) = square root of (x2 – x1)the whole square + (y2 – y1)the
whole square
Probability
probability = number of favorable outcomes /numbers of possible outcomes
Data and Graphs
dot diagram
Mode  peak value or most common value (the most frequent data)
Cluster  a place with lots of data surrounding
Outliers or extreme value  the uncommon data (too high or too low)
Spread of the data  range of the data
stem and leaf diagram
must include  key
must be  ascending order
Important factors
Mode = most common value
Median = middle number
Mean = average
Range = difference between the start and the end (not included in average)