Geometry: Formulas and Theorems

Triangles

• Area = (1/2) × base × height
• Area = √[s(s-a)(s-b)(s-c)] (Heron's formula, s = semi-perimeter)
• Pythagoras: a² + b² = c² (right triangle)
• Sum of angles = 180°

Circles

• Circumference = 2πr
• Area = πr²
• Arc length = (θ/360) × 2πr
• Sector area = (θ/360) × πr²
• Chord distance from center: d² + (chord/2)² = r²

Quadrilaterals

• Rectangle: Area = l × b, Perimeter = 2(l + b)
• Square: Area = a², Perimeter = 4a, Diagonal = a√2
• Parallelogram: Area = base × height
• Trapezium: Area = (1/2) × (sum of parallel sides) × height

Important Theorems

• Angle in semicircle = 90°
• Angles in same segment are equal
• Tangent perpendicular to radius at point of contact
• Two tangents from external point are equal

CAT Strategy

Draw diagrams for every geometry question - visualizing saves time.