Lesson 2: Angles, Polygons, Triangles, and Quadrilaterals

Angles

• Perpendicular Lines:
  • Two lines that intersect to form four right angles (90 degrees).
• Straight Angle:
  • An angle of 180 degrees, a flat line.
• Types of Angles:
  • Acute Angles: Less than 90 degrees.
  • Obtuse Angles: Greater than 90 degrees.
  • Right Angle: Exactly 90 degrees.
• Supplementary Angles:
  • Two angles that add up to 180 degrees.
• Full Circle:
  • A total of 360 degrees.

Polygons

• Definition:
  • A closed flat geometric figure with sides that are line segments.
• Non-Polygons:
  • Shapes that cross in the middle or are not fully connected.
  • Shapes with curved lines.

Naming Polygons

• Triangle: 3 sides
• Quadrilateral: 4 sides
• Pentagon: 5 sides
• Hexagon: 6 sides
• Heptagon: 7 sides
• Octagon: 8 sides
• Nonagon: 9 sides
• Decagon: 10 sides
• Undecagon: 11 sides
• Dodecagon: 12 sides
• N-gon: N sides

Types of Polygons

• Concave:
  • Has an indentation, or a "cave".
• Convex:
  • All vertices point outward.

Regular Polygons

• Equilateral: All sides are equal.
• Equiangular: All angles are equal.
• Regular Polygon: Both equilateral and equiangular.

Types of Triangles

• Right Triangle: One angle is 90 degrees.
• Obtuse Triangle: One angle is greater than 90 degrees.
• Acute Triangle: All angles are less than 90 degrees.
• Scalene Triangle: All sides of different lengths.
• Isosceles Triangle: Two sides of equal length.
  • Base angles are equal.
• Equilateral Triangle: All sides and angles are equal.

Triangle Properties

• Triangle Sum Formula:
  • All angles in a triangle add up to 180 degrees.

Solving for Unknown Angles

• Use the properties of triangles to find missing angles by setting up equations or subtracting from 180 degrees.

Quadrilaterals

• Parallelogram: Opposite sides are parallel.
• Rhombus: All sides are equal and opposite sides are parallel.
• Trapezoid: At least one pair of parallel sides.
• Square: All sides equal, all angles 90 degrees.

Key Concepts

• Square vs Rhombus:
  • A square can be a rhombus, but not all rhombuses are squares.