Geometry EOC Prep

Geometry EOC Prep

Circles and Circle Theorems

• Circle properties:
  • Center: midpoint of a diameter
  • Radius: distance from center to any point on the circle
  • Diameter: longest possible chord, passes through center
• Circle theorems:
  • Inscribed angle theorem: angle at the center of a circle is twice the inscribed angle
  • Central angle theorem: angle at the center of a circle is equal to the sum of the inscribed angles
  • Intercepted arc theorem: the angle at the center of a circle is equal to the sum of the intercepted arcs

Right Triangles and Trigonometry

• Right triangle properties:
  • Hypotenuse: longest side, opposite the right angle
  • Legs: sides that meet at the right angle
• Trigonometric ratios:
  • Sine (sin): opposite side / hypotenuse
  • Cosine (cos): adjacent side / hypotenuse
  • Tangent (tan): opposite side / adjacent side
• Pythagorean identity: sin^2(A) + cos^2(A) = 1

Properties of Congruent and Similar Figures

• Congruent figures:
  • Same shape and size
  • Corresponding angles and sides are equal
• Similar figures:
  • Same shape, different size
  • Corresponding angles are equal, corresponding sides are proportional
• Criteria for congruence and similarity:
  • SAS (side-angle-side), ASA (angle-side-angle), SSS (side-side-side) for congruence
  • AA (angle-angle) for similarity

Angles and Measurement

• Angle properties:
  • Complementary angles: add up to 90°
  • Supplementary angles: add up to 180°
  • Vertical angles: formed by two intersecting lines
• Angle measurement:
  • Degrees: 360° in a circle, 180° in a straight angle
  • Radians: 2π in a circle, π in a straight angle

Points, Lines, and Planes

• Point: location in space, represented by an ordered pair (x, y)
• Line: set of points extending infinitely in two directions
• Plane: set of points extending infinitely in all directions
• Intersections:
  • Two lines intersect at a point
  • A line and a plane intersect at a line
  • Two planes intersect at a line

Volume and Surface Area of 3D Shapes

• Volume:
  • Rectangular prism: V = lwh
  • Cylinder: V = πr^2h
  • Cone: V = (1/3)πr^2h
• Surface area:
  • Rectangular prism: SA = 2(lw + lh + wh)
  • Cylinder: SA = 2πr(h + r)
  • Cone: SA = πr(r + l)

Weighted Average

• Weighted average formula: (Σ(xi * wi)) / Σwi
• xi: individual data points
• wi: weights assigned to each data point

Transformations, Rotations, and Dilatations

• Transformations:
  • Translation: movement in a straight line
  • Reflection: flip over a line
  • Rotation: turn around a fixed point
• Rotations:
  • Center of rotation: fixed point around which the rotation occurs
  • Angle of rotation: measure of the rotation
• Dilatations:
  • Scale factor: multiplier applied to each dimension
  • Center of dilation: fixed point around which the dilation occurs