Geometry EOC Notes

Geometry Terms

• Point: Indicated with a dot and labeled with a letter (e.g., A).
• Ray: A part of a line that starts at a point and goes on forever in one direction.
• Line Segment: A part of a line having two end points.
• Line: Goes on forever in both directions.
• Intersecting Lines: Two lines that meet or intersect.
• Perpendicular Lines: Two lines that meet (intersect) at right angles.
• Parallel Lines: Two lines that will never intersect.

Trigonometric Ratios

• SOH-CAH-TOA: Mnemonic for trigonometric ratios.
• Trigonometric ratios are the ratio of 2 sides of a right triangle.
  • Sine (Sin)
  • Cosine (Cos)
  • Tangent (Tan)
• Definitions:
  • $Sin A = \frac{Opp}{hyp}$
  • $Cos A = \frac{adj}{hyp}$
  • $Tan A = \frac{Opp}{adj}$
• Reciprocal Trigonometric Ratios:
  • Cosecant (csc) is the reciprocal of Sine (sin).
  • Secant (sec) is the reciprocal of Cosine (cos).
  • Cotangent (cot) is the reciprocal of Tangent (tan).

Parallel Lines Cut by a Transversal

• Adjacent Angles: Form a straight line and are supplementary.
  • Example: $\angle 1 + \angle 2 = 180^{\circ}$
• Vertical Angles: Always equal.
  • Example: $\angle 1 = \angle 4$
• Corresponding Angles: Angles coincide with each other if lines are moved.
  • Example: $\angle 2 = \angle 6$
• Alternate Interior Angles:
  • Example: $\angle 1 = \angle 5$
• Consecutive Interior Angles:
  • Inside parallel lines & supplementary.
• Interior Angles: Inside parallel lines.
• Exterior Angles: Outside parallel lines.
• Same Side of Transversal:.
• Opposite Sides of Transversal:

Geometry: Angles, Triangles, and Parallelograms

• Angles
  • $a + b + c + d = 180$ : Sum of angles on one side of a transversal.
  • $a + b = 180$: Supplementary angles.
  • $a + b + c + d = 360$: Sum of angles around a point.
• Angles intersect vertically.
• Corresponding angles are equal.
• Alternate angles are equal.
• Interior angles.
• Triangles
  • Equilateral: 3 equal sides.
  • Isosceles: 2 equal sides.
  • Scalene: No equal sides.
  • Right triangle.

Trigonometry

• Trigonometry deals with the relationships between the angles and the lengths of the sides of triangles.
• Angles in trigonometry are usually indicated using Greek letters:
  • theta $\theta$
  • beta $\beta$
  • alpha $\alpha$
  • phi $\phi$
• Pythagorean Theorem
  • In a right triangle with sides a, b, and hypotenuse c:
  • $c^2 = a^2 + b^2$
  • $a^2 = c^2 - b^2$
  • $b^2 = c^2 - a^2$
• Labeling sides of a right triangle:
  • Opposite: The side opposite to the main angle.
  • Adjacent: The side leftover next to the main angle.
  • Hypotenuse: The longest side (opposite the right angle).
• Trigonometric Ratios
  • Applied to a right triangle
  • Sine: $\sin = \frac{opposite}{hypotenuse}$
  • Cosine: $\cos = \frac{adjacent}{hypotenuse}$
  • Tangent: $\tan = \frac{opposite}{adjacent}$