milestones formula sheet for geometry

Olvin

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11-01-2025

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This formula sheet covers key geometric concepts and formulas typically encountered throughout a geometry curriculum. It's designed to be a handy reference for students, providing a concise overview of essential information. Remember to always understand the underlying concepts, not just memorize the formulas.

I. Basic Shapes and Their Properties

A. Triangles:

• Area: (1/2) * base * height
• Perimeter: Sum of all three sides
• Pythagorean Theorem (Right Triangles): a² + b² = c² (where a and b are legs, and c is the hypotenuse)
• Types of Triangles:
  • Equilateral: All sides and angles are equal (60° each).
  • Isosceles: Two sides and two angles are equal.
  • Scalene: All sides and angles are different.
  • Right: One angle is 90°.
  • Acute: All angles are less than 90°.
  • Obtuse: One angle is greater than 90°.

B. Quadrilaterals:

• Rectangle: Four right angles, opposite sides equal and parallel.
  • Area: length * width
  • Perimeter: 2 * (length + width)
• Square: Four right angles, all sides equal.
  • Area: side²
  • Perimeter: 4 * side
• Parallelogram: Opposite sides equal and parallel.
  • Area: base * height
  • Perimeter: 2 * (side a + side b)
• Rhombus: All sides equal, opposite angles equal.
  • Area: base * height
  • Perimeter: 4 * side
• Trapezoid: One pair of parallel sides (bases).
  • Area: (1/2) * (base1 + base2) * height
  • Perimeter: Sum of all four sides

C. Circles:

• Area: πr² (where r is the radius)
• Circumference: 2πr or πd (where d is the diameter)
• Diameter: 2r
• Arc Length: (θ/360°) * 2πr (where θ is the central angle in degrees)
• Area of a Sector: (θ/360°) * πr² (where θ is the central angle in degrees)

II. Three-Dimensional Shapes

A. Rectangular Prisms (Cuboids):

• Volume: length * width * height
• Surface Area: 2 * (lw + lh + wh)

B. Cubes:

• Volume: side³
• Surface Area: 6 * side²

C. Cylinders:

• Volume: πr²h (where h is the height)
• Surface Area: 2πr² + 2πrh

D. Spheres:

• Volume: (4/3)πr³
• Surface Area: 4πr²

E. Cones:

• Volume: (1/3)πr²h
• Surface Area: πr² + πr√(r² + h²)

III. Advanced Concepts (Often Introduced Later)

• Similar Triangles: Corresponding angles are equal, and corresponding sides are proportional.
• Trigonometric Ratios (SOH CAH TOA): sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
• Coordinate Geometry: Distance formula, midpoint formula, slope formula, equation of a line.
• Surface Area and Volume of other 3D shapes: Pyramids, etc.

This formula sheet is a starting point. Consult your textbook and class notes for a more thorough understanding of each concept and its applications. Remember that practice is key to mastering geometry!