Elementary Math‎ > ‎

## Notes

### Congruency

*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 solids

Area/Surface Area

Volume/Mass

It is important to note the units
• of length: mm, cm, m
• of area: mm2, cm2, m2
• of volume: mm3, cm3, m3

• If the scale factor for lengths is x, then the scale factor for areas is x2, and the scale factor for volumes is x3.
• 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 units2 and the volume is 50 units3
• the area of the cuboid on the right is 22 x 20 = 160 units2
• the volume of the cuboid on the right is 23 x 50 units3 = 400 units3
• 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 units2 and the volume is 540 units3
• the area of the cuboid on the left is 180/32 = 20 units2
• the volume of the cuboid on the left is 540/33 = 20 units3