Geometry Trig

SAT Math — Geometry and Basic Trigonometry ## What to Expect Geometry accounts for about 15% of SAT Math questions. The test provides a reference sheet with key formulas (area, volume, special right triangles), but you still need to know when and how to use them. ## Area and Perimeter Formulas (provided on test, but memorize anyway) | Shape | Area | Perimeter/Circumference | |---|---|---| | Rectangle | l × w | 2l + 2w | | Triangle | ½ × base × height | Sum of sides | | Circle | πr² | 2πr (circumference) | | Trapezoid | ½(b₁ + b₂) × h | Sum of sides | Volume formulas provided: - Rectangular prism: V = l × w × h - Cylinder: V = πr²h - Cone: V = ⅓πr²h - Sphere: V = ⁴⁄₃πr³ - Pyramid: V = ⅓ × base area × height ## Angle Rules Triangles: Angles sum to 180°. Straight line: Angles on one side of a line sum to 180°. Vertical angles: Equal (formed by two intersecting lines). Parallel lines cut by a transversal: - Alternate interior angles: equal - Corresponding angles: equal - Co-interior (same-side interior) angles: supplementary (sum to 180°) ## Special Right Triangles (Memorize These!) 30-60-90 triangle: Sides in ratio 1 : √3 : 2 - Short leg (opposite 30°) = x - Long leg (opposite 60°) = x√3 - Hypotenuse = 2x 45-45-90 triangle: Sides in ratio 1 : 1 : √2 - Legs = x - Hypotenuse = x√2 ## Pythagorean Theorem a² + b² = c² (c = hypotenuse) Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17 (and multiples: 6-8-10, etc.) ## Basic Trigonometry (SOH CAH TOA)…