Geometry and Statistics Basics

Geometry

• Branch of mathematics dealing with the study of shapes, sizes, and positions of objects
• Involves points, lines, angles, and planes
• Key concepts:
  • Points: locations in space, represented by coordinates (x, y, z)
  • Lines: sets of points extending infinitely in two directions
  • Angles: formed by two rays sharing a common endpoint (vertex)
  • Planes: flat surfaces that extend infinitely in all directions

Statistics

• Branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data
• Involves:
  • Descriptive statistics: summarizing and describing data
  • Inferential statistics: making conclusions about a population based on a sample
• Key concepts:
  • Measures of central tendency: mean, median, mode
  • Measures of variability: range, variance, standard deviation
  • Probability: chance of an event occurring

Construction of Angle 60 and 90 Degrees

Construction of 60 Degrees Angle

• Method 1: Using a Compass

  1. Draw a line segment AB
  2. Place the point of the compass on A and draw an arc above AB
  3. Place the point of the compass on B and draw an arc that intersects the first arc
  4. Draw a line through the point of intersection and A, creating a 60-degree angle

• Method 2: Using a Ruler and a Set Square

  1. Draw a line segment AB
  2. Place the set square on the line, with one arm on the line and the other arm at a 30-degree angle
  3. Draw a line along the 30-degree arm, creating a 60-degree angle

Construction of 90 Degrees Angle

• Method 1: Using a Compass

  1. Draw a line segment AB
  2. Place the point of the compass on A and draw an arc above AB
  3. Place the point of the compass on B and draw an arc that intersects the first arc
  4. Draw a line through the point of intersection and A, creating a 90-degree angle

• Method 2: Using a Ruler and a Set Square

  1. Draw a line segment AB
  2. Place the set square on the line, with one arm on the line and the other arm at a 90-degree angle
  3. Draw a line along the 90-degree arm, creating a 90-degree angle