Angles
Complementary: sum = 90°
Supplementary: sum = 180°
Triangle sum: A+B+C = 180°
Exterior angle: = sum of remote interior
Vertical angles: equal
Triangles
Pythagorean: a²+b²=c²
Area: ½ × base × height
Perimeter: a+b+c
Similar: sides proportional
3-4-5, 5-12-13 common triples
Circles
Area: π r²
Circumference: 2πr
Diameter: d = 2r
Arc length: (θ/360)×2πr
Polygons & 3D
Interior sum: (n–2)×180°
Rectangle area: l×w
Trapezoid area: ½(b₁+b₂)×h
Cube volume: s³
Cylinder vol: πr²h
Coordinate Geometry
Distance: √((x₂-x₁)²+(y₂-y₁)²)
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
Slope: (y₂-y₁)/(x₂-x₁)
Parallel Lines
Alternate interior: equal
Corresponding: equal
Co-interior (same-side): sum = 180°
⭐ Must Memorize
- Pythagorean Triples: (3,4,5) · (5,12,13) · (8,15,17) — all multiples also work
- Interior angle sum of polygon with n sides = (n−2) × 180°
- Exterior angle of a triangle = sum of the two non-adjacent interior angles
- Vertical angles are always equal; supplementary angles sum to 180°
- Co-interior (same-side) angles between parallel lines sum to 180°
- Surface area of cube = 6s²; Volume of cube = s³
✏ Quick Example
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
Answer: c = √(6² + 8²) = √(36+64) = √100 = 10