NotesCongruency *3 tests required SSS (3 Sides)  All 3 sides are equal
 SAS (Side  Angle  Side)  2 sides are equal, included angle equal
 AAS (Angle  Angle  Angle)  2 angles equal, included side equal
 RHS (Right Angle Hyp. Side)  Longest side of triangle equal, 1 angle equal
Similarity*2 tests required RRR (3 Sides)  3 sides equal proportions
 AAA (3 Angles)  3 angles equal
 RAR (Ratio  Angle  Ratio)  2 sides equal proportion, included angle equal
Area/Volume of similar solidsArea/Surface AreaVolume/MassIt is important to note the units  of length: mm, cm, m
 of area: mm^{2}, cm^{2}, m^{2}
 of volume: mm^{3}, cm^{3}, m^{3}
 If
the scale factor for lengths is x, then the scale factor for areas is x^{2}, and the scale factor for volumes is x^{3}.
 All the length of the sides of the solid on the right
are twice the lengths of corresponding sides on the left.
 If the area of the cuboid on the left is 20 units^{2} and the volume is 50 units^{3}
 the area of the cuboid on the right is 2^{2} x 20 = 160 units^{2}
 the volume of the cuboid on the right is 2^{3} x 50 units^{3} = 400 units^{3}

All the length of the sides on the right are 3 times the lengths of corresponding sides on the left
 If the area of the cuboid on the right is 180 units^{2} and the volume is 540 units^{3}
 the area of the cuboid on the left is 180/3^{2} = 20 units^{2}
 the volume of the cuboid on the left is 540/3^{3} = 20 units^{3}
