Arc length s = rθ, where θ is in radians and r is the radius. This is the most elegant arc length formula.

Two tangent segments drawn from an external point to a circle are always equal in length.

A transversal is a line that crosses two or more other lines at different points, creating angles like alternate interior, corresponding, etc.

Triangle Inequality: the sum of any two sides of a triangle must be greater than the third side.

Perimeter of rectangle = 2l + 2w = 2(l + w). Add all four sides.

Each angle in an equilateral triangle = 60°. Sum = 180°, divided equally among 3 equal angles.

Area = πr² = π(d/2)² = πd²/4. Since r = d/2, substitute to get the diameter version.

A median connects a vertex to the midpoint of the opposite side. The three medians meet at the centroid.

Volume of rectangular prism = length × width × height.

Perimeter of semicircle = πr + 2r (curved arc + diameter). The diameter is the straight edge.

Area of parallelogram = base × height. The height must be perpendicular to the base.

A midsegment connects midpoints of two sides. It is parallel to the third side and half its length.

Volume of hemisphere = (2/3)πr³. It is exactly half the volume of a full sphere (4/3)πr³.

Regular pentagon interior angle = (5-2)×180°/5 = 540°/5 = 108°.

In 30-60-90: shorter leg = a, longer leg = a√3, hypotenuse = 2a.

To convert degrees to radians: multiply by π/180. To convert radians to degrees: multiply by 180/π.

Perimeter of regular hexagon = 6s. A regular hexagon has 6 equal sides.

Total SA = 2(lw + lh + wh). Add all 6 faces: 2 of each pair of opposite faces.

Volume of cylinder = πr²h. Think of it as the area of the circular base (πr²) times the height.

Volume of triangular prism = base area × height (length). Base area = ½bh of the triangular cross-section.