Geometry And Trigonometry Sat Cheat Sheet

Your Ultimate SAT Geometry and Trigonometry Cheat Sheet: Formulas, Strategies, and Core Concepts

Conquering the SAT Math section isn't about secret tricks; it's about strategic mastery of a defined set of concepts. The digital SAT, with its adaptive format, tests your ability to apply fundamental geometry and trigonometry principles efficiently under time pressure. This comprehensive guide serves as your definitive SAT geometry and trigonometry cheat sheet, distilling everything you need into a powerful, actionable reference. Move beyond rote memorization—this resource is designed to build the intuitive understanding required to recognize patterns, set up problems correctly, and select the right tool for any question, transforming anxiety into confident execution.

Part 1: Plane Geometry – The Foundational Framework

Plane geometry forms the bedrock of SAT spatial reasoning. You must be fluent in properties of shapes, angle relationships, and area/perimeter calculations.

Essential Triangle Properties

• Angle Sum: The interior angles of any triangle sum to 180°.
• Triangle Inequality Theorem: The sum of the lengths of any two sides must be greater than the length of the third side.
• Isosceles Triangle: Two equal sides ↔ two equal base angles. The altitude to the base bisects the base and the vertex angle.
• Equilateral Triangle: All sides and angles (60° each) are equal. Height = (side * √3)/2.
• Special Right Triangles (CRITICAL):
  • 45°-45°-90°: Sides in ratio 1 : 1 : √2 (leg : leg : hypotenuse).
  • 30°-60°-90°: Sides in ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). The hypotenuse is always twice the short leg.

Key Angle Theorems & Relationships

• Vertical Angles: Opposite angles formed by two intersecting lines are congruent.
• Corresponding Angles: When a transversal crosses parallel lines, corresponding angles are congruent.
• Alternate Interior/Exterior Angles: When a transversal crosses parallel lines, these angles are congruent.
• Same-Side Interior Angles: When a transversal crosses parallel lines, these angles are supplementary (sum to 180°).
• Polygon Interior Angles: Sum = (n - 2) * 180°, where n = number of sides.
• Polygon Exterior Angles: Sum is always 360°, regardless of n.

Area & Perimeter Formulas

• Triangle: Area = ½ * base * height. Also, Area = ½ * ab * sin(C) for any two sides a, b and included angle C.
• Rectangle/Parallelogram: Area = base * height. For a parallelogram, the height is the perpendicular distance between bases.
• Trapezoid: Area = ½ * (base₁ + base₂) * height.
• Circle: Circumference = 2πr or πd. Area = πr².
• Sector of a Circle: `Area = (θ/360°)