Pythagoras + Special Right Triangles
Right triangle: legs a and b, hypotenuse c → a² + b² = c².
45-45-90 triangle: both legs equal, hypotenuse = leg × √2.
30-60-90 triangle: sides opposite 30° is shortest (x), opposite 60° is x√3, hypotenuse 2x.
Quadrilaterals
Parallelogram: both pairs of opposite sides parallel and equal in length.
Rectangle: parallelogram with all right angles.
Rhombus: parallelogram with all sides the same length.
Square: both rectangle and rhombus (all sides equal + all angles 90°).
Trapezoid: exactly one pair of parallel sides.
Circle Theorems (main ones)
Angle at the center is twice the angle at the circumference when they stand on the
same arc.
Angles standing on the same arc (in the same segment) are equal.
Angle in a semicircle is always 90°.
Tangent line meets radius at 90° (perpendicular).
Opposite angles in a cyclic quadrilateral add to 180°.
Area Formulas
Triangle: half × base × height, or half × side × side × sin(included angle).
Rectangle: length × width.
Parallelogram: base × perpendicular height.
Trapezoid: half × (sum of parallel sides) × height.
Circle: π × radius squared.
Sector: (angle/360) × π × radius squared.
Volume Basics
Prism or cylinder: area of base × height.
Cone: one-third × π × radius squared × height.
Sphere: four-thirds × π × radius cubed.
Sphere surface area: 4 × π × radius squared.
Right triangle: legs a and b, hypotenuse c → a² + b² = c².
45-45-90 triangle: both legs equal, hypotenuse = leg × √2.
30-60-90 triangle: sides opposite 30° is shortest (x), opposite 60° is x√3, hypotenuse 2x.
Quadrilaterals
Parallelogram: both pairs of opposite sides parallel and equal in length.
Rectangle: parallelogram with all right angles.
Rhombus: parallelogram with all sides the same length.
Square: both rectangle and rhombus (all sides equal + all angles 90°).
Trapezoid: exactly one pair of parallel sides.
Circle Theorems (main ones)
Angle at the center is twice the angle at the circumference when they stand on the
same arc.
Angles standing on the same arc (in the same segment) are equal.
Angle in a semicircle is always 90°.
Tangent line meets radius at 90° (perpendicular).
Opposite angles in a cyclic quadrilateral add to 180°.
Area Formulas
Triangle: half × base × height, or half × side × side × sin(included angle).
Rectangle: length × width.
Parallelogram: base × perpendicular height.
Trapezoid: half × (sum of parallel sides) × height.
Circle: π × radius squared.
Sector: (angle/360) × π × radius squared.
Volume Basics
Prism or cylinder: area of base × height.
Cone: one-third × π × radius squared × height.
Sphere: four-thirds × π × radius cubed.
Sphere surface area: 4 × π × radius squared.
